Upcoming SlideShare
×

# Maths A - Chapter 01

12,569 views

Published on

Year 11 Maths A Textbook - Chapter 1 out of 12

3 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
12,569
On SlideShare
0
From Embeds
0
Number of Embeds
14
Actions
Shares
0
79
0
Likes
3
Embeds 0
No embeds

No notes for slide

### Maths A - Chapter 01

1. 1. 1syllabussyllabusrrefefererenceence Strand: Financial mathematics Core topic: Managing money 1 • Earning money In thisIn this chachapterpter 1A Calculating salary payments 1B Calculating wages 1C Commission and royalties 1D Payment by piece 1E Working overtime 1F Additions to and deductions from gross pay Earning money MQ Maths A Yr 11 - 01 Page 1 Wednesday, July 4, 2001 2:17 PM
2. 2. 2 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Introduction Karla will ﬁnish school in three months and has plans of joining the workforce. She has never had paid employment before. Many of her friends have part-time work and talk about ‘pay rates’, ‘overtime’ and ‘tax’ — it is all a mystery to her. Karla should know about these things because, in the end, she is the only person to look out for her own best interests. Is she paid at the correct rate? Are the pay calculations accurate? Is she paying the appropriate tax? Is she maximising her income? 1 Calculate 25% of 300. 2 What is 4.5% of 280? 3 Reduce 4500 by 15%. 4 Write 25 out of 220 as a percentage. 5 A car travels at 80 km/h. How far does it travel in 5 hours at this speed? 6 A man assembles 24 machines in one day. How long will it take him to assemble 500 machines at this rate? Let us begin to answer Karla’s questions. She will ﬁnd that different occupations may calculate pay in different ways. Calculating salary payments Methods of payment A payment received by an employee for doing a job is called income. There are many different ways people are paid for performing a job. In this section we are going to look at some of these methods of payment: salaries, wages, commission, royalties, piecework and overtime. Perhaps after some further study, Karla will take up a professional occupation. In this case she will probably be paid a salary. Salaries Many people employed in professional occupations are paid a salary. Such employees include teachers, lawyers, accountants and some doctors. A lecturer is paid a salary. SkillS HEET 1.1 SkillS HEET 1.2 SkillS HEET 1.3 MQ Maths A Yr 11 - 01 Page 2 Friday, July 6, 2001 9:40 AM
3. 3. C h a p t e r 1 E a r n i n g m o n e y 3 A salary is a ﬁxed amount of money that is paid to employees to do their jobs. The amount paid does not change, regardless of the number of hours worked. Salaries are usually calculated on an annual basis. A salary is therefore usually stated as an amount per annum, which means per year. Salaries are paid in weekly, fortnightly or monthly amounts. To make calculations about salaries you will need to remember the following information. 1 year = 52 weeks = 26 fortnights = 12 months We reverse this calculation when we are given the weekly, fortnightly or monthly pay of a person and are then asked to calculate the annual salary. To compare a salary payment with other forms of income it may be necessary to calcu- late the equivalent daily or hourly payment. To do this we need to know the number of days or hours worked per week. Dimitri works as an accountant and receives an annual salary of \$46 800. Calculate the pay that Dimitri is paid each fortnight. THINK WRITE There are 26 fortnights in a year, so we divide \$46 800 by 26. Fortnightly pay = \$46 800 ÷ 26 Evaluate. Fortnightly Pay = \$1800 1WORKEDExample Grace is a solicitor who is paid \$3500 per month. Calculate Grace’s annual salary. THINK WRITE There are 12 months in a year, so multiply \$3500 (monthly pay) by 12. Annual salary = \$3500 × 12 Evaluate. Annual salary = \$42 000 1 2 2WORKEDExample Charlotte works as a laboratory technician and is paid an annual salary of \$41 560. If Charlotte works an average of 42 hours per week, calculate her equivalent hourly rate of pay. THINK WRITE Calculate the weekly pay by dividing the salary by 52. Weekly pay = \$41 560 ÷ 52 = \$799.23 Calculate the hourly rate by dividing the weekly pay by 42. Hourly rate = \$799.23 ÷ 42 = \$19.03 1 2 3WORKEDExample MQ Maths A Yr 11 - 01 Page 3 Wednesday, July 4, 2001 2:17 PM
4. 4. 4 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Calculating salary payments 1 Toni is paid a salary of \$44 200 per annum. Calculate Toni’s fortnightly pay. 2 Roger is paid a salary of \$49 920 per annum. Calculate Roger’s weekly pay. 3 Frieda is paid a salary of \$54 000 per annum. Calculate Frieda’s monthly pay. 4 Wendy works as an ofﬁce secretary and is paid a salary of \$38 740 per annum. Calculate Wendy’s pay if she is paid: a weekly b fortnightly c monthly. 5 Darren earns a salary of \$43 000 per annum. Calculate Darren’s fortnightly pay correct to the nearest cent. 6 Copy and complete the table below for food production employees. 7 Maxine is paid a salary. She receives \$460 per week. Calculate Maxine’s annual salary. 8 Thao receives \$1250 per fortnight. Calculate Thao’s annual salary. 9 Deidre is paid monthly and receives \$5800. Calculate Deidre’s annual salary. Annual salary Weekly pay Fortnightly pay Monthly pay \$30 000 \$39 500 \$42 250 \$54 350 \$86 475 remember 1. A salary is a ﬁxed payment made for doing a job. 2. A salary is usually calculated on an annual basis and can be paid in weekly, fortnightly or monthly instalments. 3. To calculate information about equivalent daily or hourly rates of pay we need information about the number of days and hours worked by the employee. remember 1A WORKED Example 1 WORKED Example 2 MQ Maths A Yr 11 - 01 Page 4 Wednesday, July 4, 2001 2:17 PM
6. 6. 6 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Using a similar method we are able to calculate the number of hours worked by an employee, given their wage and hourly rate of pay. The number of hours worked is found by dividing the wage by the hourly rate. In some cases, wages are increased because an allowance is paid for working in unfavourable conditions. An allowance is an additional payment made when the working conditions are difﬁcult or unpleasant. For example, a road worker may be paid an allowance for working in the rain. In these cases the allowance must be multiplied by the number of hours worked in the unfavourable conditions and this amount added to the normal pay. This type of allowance is also paid to casual workers. When you are employed on a casual basis you do not receive any holiday pay and you do not get paid for days you have off because you are sick. The casual rate is a higher rate of pay to compensate for this. Georgina works 42 hours as a data entry operator for a computer company. Her wage for the week totalled \$483.84. Calculate Georgina’s hourly rate of pay. THINK WRITE Divide \$483.84 (the wage) by 42 (number of hours worked). Hourly rate = \$483.84 ÷ 42 Hourly rate = \$11.52 5WORKEDExample Ryan is a road worker and is paid \$9.45 per hour for a 35-hour week. For working on wet days he is paid a wet weather allowance of 86c per hour. Calculate Ryan’s pay if for 12 hours of the week he works in the rain. THINK WRITE Calculate Ryan’s normal pay by multiplying \$9.45 (hourly rate) by 35 (number of hours worked). Normal pay = \$9.45 × 35 = \$330.75 Calculate the wet weather allowance by multiplying 0.86 (the wet weather allowance) by 12 (number of hours worked in the wet). Allowance = \$0.86 × 12 = \$10.32 Add the normal pay to the wet weather allowance to calculate the total pay. Total pay = \$330.75 + \$10.32 = \$341.07 1 2 3 6WORKEDExample MQ Maths A Yr 11 - 01 Page 6 Wednesday, July 4, 2001 2:17 PM
7. 7. C h a p t e r 1 E a r n i n g m o n e y 7 Calculating wages 1 Allan works in a newspaper printing mill and is paid \$12.95 per hour. Calculate Allan’s wage in a week where he works 40 hours. 2 Copy and complete the table below by calculating the wage of each of the workers. 3 Alicia is an apprentice chef. In the ﬁrst year of her apprenticeship she earns \$11.80 per hour. Calculate Alicia’s wage in a week where she works: a 36 hours b 48 hours c 42.5 hours. 4 Domonic is a fully qualiﬁed chef. He earns \$13.50 per hour. Calculate Domonic’s wage in a week where he works: a 32 hours b 37 hours c 44.5 hours. Name Hourly rate Hours worked Wage A. Smith \$14.52 40 B. Brown \$16.45 38 N. Tran \$15.95 37.5 A. Milo \$20.10 41 L. McTavish \$18.04 36 remember 1. A wage is money earned at an hourly rate. 2. To calculate a wage we multiply the hourly rate by the number of hours worked during the week. 3. To calculate an hourly rate we divide the wage by the number of hours worked. 4. To calculate the number of hours worked we divide the wage by the hourly rate. 5. Allowances are paid for working under unfavourable conditions. The total allowance should be calculated and then added to the normal pay. 6. A casual rate is a higher rate of pay for casual workers to compensate them for having no holidays and receiving no sick leave. remember 1B WORKED Example 4 MQ Maths A Yr 11 - 01 Page 7 Wednesday, July 4, 2001 2:17 PM
8. 8. 8 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 5 Katherine works as a casual waitress. Casual workers earn 20% more per hour than full-time workers to compensate for their lack of holidays and sick leave. a A full-time waitress earns \$14.45 per hour. Calculate the casual rate earned by casual waitresses. b Calculate Katherine’s wage in a week where she works 6 hours on Saturday and 7 hours on Sunday. 6 Which of the following workers earns the highest wage for the week? A Dylan, who works 35 hours at \$13.50 per hour B Lachlan, who works 37 hours at \$12.93 per hour C Connor, who works 38 hours at \$12.67 per hour D Cameron, who works 40 hours at \$12.19 per hour 7 Calculate the hourly rate of a person who works 40 hours for a wage of \$387.20. 8 Julie earns \$11.42 per hour. Calculate the number of hours worked by Julie in a week where she is paid \$445.38. 9 Copy and complete the table below. 10 Calculate the hourly rate of a casual worker who earns \$250.80 for 20 hours work. 11 Which of the following workers is paid at the highest hourly rate? A Melissa, who works 35 hours for \$366.45 B Belinda, who works 36 hours for \$376.20 C April, who works 38 hours for \$399.76 D Nicole, who works 40 hours for \$419.60 12 Which of the following people worked the greatest number of hours? A Su-Li, who earned \$439.66 at \$11.57 per hour. B Denise, who earned \$576.00 at \$14.40 per hour. C Vera, who earned \$333.20 at \$9.52 per hour. D Camille, who earned \$707.25 at \$17.25 per hour. 13 Richard works as an electrical linesman and is paid \$10.94 per hour for a 38-hour week. When he has to work at heights he is paid a 46c per hour ‘height allowance’. Calculate Richard’s pay in a week where 15 hours are spent working at heights. Name Wage Hours worked Hourly rate A. White \$416.16 36 B. Black \$538.80 40 C. Green \$369.63 37 D. Brown \$813.96 \$19.38 E. Scarlet \$231.30 \$15.42 F. Grey \$776.72 \$20.44 mmultiple choiceultiple choice WORKED Example 5 mmultiple choiceultiple choice mmultiple choiceultiple choice WORKED Example 6 MQ Maths A Yr 11 - 01 Page 8 Wednesday, July 4, 2001 2:17 PM
9. 9. C h a p t e r 1 E a r n i n g m o n e y 9 14 Ingrid works as an industrial cleaner and is paid \$14.60 per hour for a 35-hour working week. When Ingrid is working with toxic substances she is paid an allowance of \$1.08 per hour. Calculate Ingrid’s pay if she works with toxic substances all week. 15 Rema works as a tailor and earns \$9.45 per hour. a Calculate Rema’s wage in a week where she works 37 hours. b Zhong is Rema’s assistant and earns \$8.20 per hour. Find the least time Zhong must work if he is to earn more money than Rema does? 16 Tamarin works 38 hours per week at \$12.40 per hour. Zoe earns the same amount each week as Tamarin does, but Zoe works a 40-hour week. Calculate Zoe’s hourly rate of pay. Spreadsheets — Wages 1 Throughout this chapter we are going to develop a number of spreadsheets that will calculate wages. Work through the following steps. 1. Open a spreadsheet and enter the following information, or download the spreadsheet (Wages_1) from the Maths Quest CD-ROM. 2. Enter a pay rate of \$11.20 per hour for each employee. 3. Enter the hours worked as follows: Frederick Astini, 40; James Carter, 38; Kelly George, 36; Dean Jones, 15; Paul Limbrick, 45. 4. In cell E7 (in the column headed Gross Pay) enter the formula =C7*D7. This will calculate the wage for Frederick Astini (the ﬁgure 448 should appear in the cell). 5. Format cell E7 as currency (cell E7 should now show \$448.00). E XCEL Spread sheet Wages 1 inv estigat ioninv estigat ion MQ Maths A Yr 11 - 01 Page 9 Wednesday, July 4, 2001 2:17 PM
10. 10. 10 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 1 Calculate the wage of a person who works 36 hours at a pay rate of \$9.56 per hour. 2 Calculate the weekly wage of a person who works 38 hours at \$13.65 per hour. 3 Donna works 15 hours on weekends at \$14.56 per hour. Calculate Donna’s wage for the weekend. 4 Calculate what Stephen will earn for working 8 hours at \$11.88 per hour. 5 Debbie earns \$489.06 for a 38-hour working week. Calculate Debbie’s hourly rate of pay. 6 Damien earns an annual salary of \$47 000 and is paid weekly. Calculate Damien’s weekly pay. 7 Simone earns an annual salary of \$70 000 and is paid fortnightly. Calculate Simone’s fortnightly pay. 8 Ivan earns an annual salary of \$56 480 and is paid monthly. Calculate Ivan’s monthly pay. 9 Penny earns an annual salary of \$44 000 and is paid weekly. Calculate Penny’s weekly pay. 10 Penny works an average of 35 hours each week. Calculate the hourly rate to which her salary is equivalent. (Answer to the nearest cent) Commission and royalties Karla likes working with people and she thinks she would be a good sales- person. In this case, Karla may be paid by commission. Commission is a method of payment used mainly for salespeople. When paid commission a person receives a percentage of the value of goods sold. A royalty is a payment made to a person who owns a copyright. For example, a musician who writes a piece of music is paid royalties on sales of CDs; an author who writes a book is paid according to the number of books sold. Royalties are calculated in the same way as a commission, being paid as a percentage of sales. 6. Highlight cells E7 to E11 and select the Fill and Down options. The wages for each employee should now be calculated and be formatted as currency. (The entries in this column should read \$448.00, \$425.60, \$403.20, \$168.00 and \$504.00.) 7. If you now change the hours worked by each employee his or her gross pay should update automatically. 8. Choose the File and Save As functions to save the spreadsheet as Wages_1. 1 MQ Maths A Yr 11 - 01 Page 10 Friday, July 6, 2001 8:28 AM
11. 11. C h a p t e r 1 E a r n i n g m o n e y 11 In some cases commission may operate on a sliding scale. This means that the com- mission rate changes with the value of sales. This type of commission is commonly used in real estate sales. In these examples each portion of the commission is calculated separately. The ﬁnal commission is the sum of each portion. Sales people often receive a ﬁxed amount (called a retainer) as well as a commission. This is to ensure that the person earns some money even if no sales are made. To calculate this type of pay you will need to add the retainer to the commission. Jack is a computer salesman who is paid a commission of 12% of all sales. Calculate the commission that Jack earns in a week if he makes sales to the value of \$15 000. THINK WRITE Calculate 12% of \$15 000. Commission = 12% of \$15 000 Commission = 12 ÷100 × \$15 000 Commission = \$1800 7WORKEDExample A real estate agent is paid com- mission on his sales at the following rate: • 5% on the ﬁrst \$75 000 • 2.5% on the balance of the sale • price. Calculate the commission earned on the sale of a property for \$235 000. THINK WRITE Calculate 5% of \$75 000. 5% of \$75 000 = \$3750 Calculate the balance of the sale. Balance = \$235 000 − \$75 000 Balance = \$160 000 Calculate 2.5% of \$160 000. 2.5% of \$160 000 = \$4000 Add up each portion to calculate the commission. Commission = \$3750 + \$4000 Commission = \$7750 1 2 3 4 8WORKEDExample MQ Maths A Yr 11 - 01 Page 11 Wednesday, July 4, 2001 2:17 PM
12. 12. 12 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d In some cases the commission does not begin to be paid until sales have reached a certain point. For example, a car salesperson may receive a commission on sales over \$5000. (Can you suggest a reason for such a payment scheme?) Here the commission is calculated only on sales above this ﬁxed amount. Shelley is a furniture salesperson and is paid \$250 per week plus a commission of 2% of all sales. Calculate Shelley’s pay in a week where her sales total \$12 250. THINK WRITE Calculate the commission of 2% of \$12 250. Commission = 2% of \$12 250 Commission = 2 ÷ 100 × 12 250 Commission = \$245 Add the \$250 to the commission to calculate her pay. Pay = \$250 + \$245 Pay = \$495 1 2 9WORKEDExample Tony is a car salesperson. Tony is paid \$300 per week and 2% of all sales over \$50 000. Calculate Tony’s pay in a week where his sales total \$84 000. THINK WRITE Calculate the amount on which commission is to be paid. \$84 000 − \$50 000 = \$34 000 Find 2% of this amount. Commission = 2% of \$34 000 Commission = 2 ÷ 100 × \$34 000 Commission = \$680 Add the \$300 to the commission to calculate Tony’s pay. Pay = \$300 + \$680 Pay = \$980 1 2 3 10WORKEDExample remember 1. A commission is earned when a person is paid a percentage of the value of sales made. 2. Some commissions are paid on a sliding scale. In these cases each portion of the commission is calculated separately and then totalled at the end. 3. Some commissions are paid together with a ﬁxed payment called a retainer. To calculate an employee’s pay the ﬁxed payment needs to be added to the commission. 4. In some cases where a ﬁxed payment is made commission may not be paid on all sales but rather, on a section of sales above a certain point. remember MQ Maths A Yr 11 - 01 Page 12 Wednesday, July 4, 2001 2:17 PM
13. 13. C h a p t e r 1 E a r n i n g m o n e y 13 Commission and royalties 1 Kylie is an insurance salesperson and she is paid 8% of the value of any insurance that she sells. Calculate the amount that Kylie is paid for selling insurance to the value of \$25 000. 2 Beryl sells exercise equipment and is paid a commission of 10% on all sales. Calculate Beryl’s earnings in a week where her sales total is: a \$2600 b \$3270 c \$5687.90 3 Darren’s job is to sell CDs to music stores. If Darren sells CDs to the value of \$40 000 calculate his commission if it is paid at a rate of: a 1% b 3% c 3.4% 4 Linda is a car salesperson who is paid 1.5% commission. Calculate the amount of money Linda earns in a week where her sales total \$95 000. 5 Ken is an author and is paid a royalty on his book sales. The royalty is 12% of the value of all sales of his book. Calculate the value of Ken’s royalty if the value of sales totals \$34 500. 6 Ursula is a computer software salesperson. Ursula’s sales total \$105 000 and she is paid a commission of 0.8%. How much does Ursula receive in commission? A \$105 B \$840 C \$8400 D \$84 000 7 Asif is a sales representative for a hardware ﬁrm. Asif earns \$870 commission on sales of \$17 400. What rate of com- mission does Asif receive? A 0.05% B 0.5% C 5% D 20% 8 A real estate agent charges commission at the following rate: • 5% on the ﬁrst \$75 000 • 2.5% on the balance of the sale price. Calculate the commission charged on the sale of a property for \$250 000. 9 Gabrielle is a fashion sales representative. Gabrielle is paid a commission of 5% on the ﬁrst \$3000 of sales each week and 10% commission on the balance. Calculate Gabrielle’s commission in a week where her sales total \$9500. 10 Using the sliding scale for commission shown in question 8, calculate the commission on a property that sells for: a \$90 000 b \$140 000 c \$600 000. 1C WORKED Example 7 mmultiple choiceultiple choice mmultiple choiceultiple choice WORKED Example 8 MQ Maths A Yr 11 - 01 Page 13 Wednesday, July 4, 2001 2:17 PM
14. 14. 14 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 11 Stanisa is a car salesman who is paid \$250 per week plus a commission of 2% of any sales he makes. Calculate Stanisa’s pay in a week where his sales total \$35 000. 12 Daniel works as a sales representative for a car accessories ﬁrm. Daniel is paid \$150 per week plus 4% of any sales. Calculate Daniel’s earnings in a week where his sales total is: a \$6000 b \$8500 c \$12 475. 13 A group of sales representatives each has \$10 000 in sales for a week. Who earns the most money? A Averil, who is paid a commission of 8% B Bernard, who is paid \$250 plus 6% commission C Cathy, who is paid \$350 plus 4% commission D Darrell, who is paid \$540 plus 2.5% commission 14 Fred and Gina sell life insurance. Fred is paid a commission of 8% and Gina is paid \$250 plus 5% commission. a How much does Fred earn for a week in which his sales are \$5000? b How much does Gina earn for a week in which her sales total \$5000? c In another week Gina earns \$650. What is the value of Gina’s sales? d Fred wishes to earn \$650 in a week. How much should his sales be? 15 Mario is a pay television salesman. Mario earns \$500 per week plus 5% commission on all sales above \$5000. Calculate Mario’s pay in a week where his sales total \$7500. 16 Neville is a door to door encyclopedia salesman. He is paid \$300 per week plus 3% commission on all sales greater than \$5000. Calculate Neville’s pay in a week where his sales total is: a \$4000 b \$6500 c \$8560. 17 A ﬁrm employs ﬁve sales representatives. Which representative will earn the most in a week where each of their sales totals \$12 480? A Peter, who receives a commission of 4% B Richard, who receives \$100 plus a commission of 3% C Susan, who is paid \$280 plus a commission of 1.8% D Trevor, who is paid \$300 plus a commission of 3.5% on all sales over \$6000 18 Andrew and Bonito are sales representatives. Andrew is paid \$300 plus a commission of 2.5% on all sales. Bonito is paid \$250 plus a 3.5% commission on all sales over \$3000. For what value of weekly sales will Andrew and Bonito receive the same pay? 19 Jade sells cosmetics, and the company pays her a ﬁxed weekly salary plus 2.5% com- mission on all sales she makes. Last week she sold \$600 worth of cosmetics and her total pay was \$490. How much would she expect to earn in a week where she sold \$1400 worth of cosmetics? 20 Rick sells security systems and is paid a weekly salary plus commission on his sales. In one week he earned \$900 when he sold security systems to the value of \$5000. In a week where he sold \$3000 worth of security systems he earned \$600. How much can he expect to earn in a week where he sells security systems to the value of \$4400? WORKED Example 9 mmultiple choiceultiple choice WORKED Example 10 mmultiple choiceultiple choice MQ Maths A Yr 11 - 01 Page 14 Wednesday, July 4, 2001 2:17 PM
15. 15. C h a p t e r 1 E a r n i n g m o n e y 15 Payment by piece Payment by piece, or piecework refers to payment for the amount of work completed. It is commonly paid for jobs such as car detailing and letterbox delivery. The amount earned is calculated by multiplying the rate of payment by the number of pieces of work completed. Which job? Karla is offered a choice of two jobs at two similar jewellery stores. Karla comes to you seeking advice. On the basis of money alone, which should she choose? This problem can be investigated in a number of ways. One useful strategy in solving questions such as these is to use guess, check and improve. This strategy is quite powerful but one needs to be systematic with it. Use the following table and complete as many guesses as you need to ﬁnd, correct to the nearest dollar, the minimum sales Karla would need to make before Pure Diamond Jeweller becomes her better option. Write a letter to Karla advising which job to take and providing evidence to support your advice. inv estigat ioninv estigat ion Pure Diamond Jeweller offers \$250 plus 3.5% commission on all sales over \$3 000. Michael Crest Jeweller offers \$300 plus 2.5% commission on all sales Guess no. Sales amount Income earned at Michael Crest Income earned at Pure Diamond Better option? 1 \$4000 \$400 \$285 MC 2 3 4 … Work SHEET 1.1 A person delivering to a letterbox is paid for piecework. MQ Maths A Yr 11 - 01 Page 15 Wednesday, July 4, 2001 2:17 PM
16. 16. 16 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d In most cases it is very clear when payment is made using a piece rate. When the person picking oranges is paid \$18 for each container ﬁlled, payment is clearly at a piece rate. Other situations are not so clear. Would you consider a doctor who receives a fee for consultation to be receiving a piece rate payment? In some cases, piecework is paid for multiples, rather than for single units. For example, if you have a job making letterbox deliveries, you may be paid per 1000 brochures that you deliver. There may also be occasions where you will want to compare the rates of pay for dif- ferent jobs. For example, you may wish to compare payment by piece with other methods of earning income, such as wages. Len has a job washing cars in a caryard. He is paid \$2.25 per car washed. Calculate what Len earns in an afternoon where he washes 24 cars. THINK WRITE Multiply the pay rate by the number of cars detailed. Pay = \$2.25 × 24 Pay = \$54.00 11WORKEDExample Holly is delivering brochures to letterboxes in her local area. She is paid \$23.00 per thou- sand brochures delivered. Calculate what Holly will earn for a delivery of 3500 brochures. THINK WRITE Divide 3500 by 1000 to calculate the number of thousand brochures delivered. 3500 ÷ 1000 = 3.5 Multiply 3.5 by \$23.00 to calculate what Holly is paid. Holly’s pay = 3.5 × \$23.00 Holly’s pay = \$80.50 1 2 12WORKEDExample Tristan has a job picking apples. He is paid \$4.40 per basket. a Calculate Tristan’s pay for picking 21 baskets of apples in one day. b If it takes Tristan 8 hours to pick these apples, calculate the equivalent hourly rate of pay he has earned. THINK WRITE a Multiply 21 (the number of baskets) by \$4.40 (the pay per basket). a Pay = 21 × \$4.40 Pay = \$92.40 b Divide \$92.40 (total pay) by 8 (number of hours worked). b Hourly rate = \$92.40 ÷ 8 Hourly rate = \$11.55 13WORKEDExample MQ Maths A Yr 11 - 01 Page 16 Wednesday, July 4, 2001 2:17 PM
18. 18. 18 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 11 Denise works as a fruit picker. She is paid \$4.20 for every basket of fruit picked. a Calculate the amount Denise will earn in a day during which she picks 32 baskets of fruit. b If it takes Denise 8 hours to pick the fruit, calculate the equivalent hourly rate of pay. 12 Charlie works in a caryard as a detailer. Charlie is paid \$11.60 per car. a What will Charlie earn in an afternoon during which he details 15 cars? b If it takes Charlie 8 hours to detail the cars, calculate his hourly rate of pay. c If Charlie could ﬁnish in 6 hours, calculate the hourly rate of pay he would earn. 13 Katie has a stall at the ﬂea market and sells CDs. She sells new CDs for \$24 and second-hand CDs for \$18. On Sunday she sold \$516 worth of CDs and noticed that she had sold 4 more new CDs than second-hand ones. How many did she sell in total? 1 Kim works a 37-hour week at a rate of \$12.32 per hour. Calculate her weekly wage. 2 Viet works 35 hours a week at an hourly rate of \$9.89 per hour. Calculate Viet’s weekly wage. 3 Samantha is paid an annual salary of \$38 500 and is paid weekly. Calculate Samantha’s weekly pay. 4 Tom is paid an annual salary of \$86 000 and is paid fortnightly. Calculate Tom’s fortnightly pay. 5 Celine is paid \$1246.40 per fortnight. Calculate her annual salary. 6 Mick is paid 7% commission on all sales he makes. Calculate his commission for a week in which his sales total \$6960. 7 Christine is paid \$250 per week plus 2.5% commission on all sales. Calculate Christine’s pay for a week in which her sales total \$12 800. 8 Jason has a job picking fruit and is paid \$4.85 per basket. Calculate Jason’s pay for a day in which he picks 43 baskets of fruit. 9 Julia has a job delivering pamphlets to letterboxes and is paid \$13.40 per 1000 pamphlets delivered. Calculate Julia’s pay for delivering 4500 pamphlets. 10 Cameron is an author who receives a royalty of 8% of the value of sales of his book. Calculate Cameron’s royalty for book sales totalling \$23 000. WORKED Example 13 2 MQ Maths A Yr 11 - 01 Page 18 Wednesday, July 4, 2001 2:17 PM
19. 19. C h a p t e r 1 E a r n i n g m o n e y 19 What should I quote? Chris is a builder who works for Creative Constructions. A customer has asked Chris to provide a quote for an extension to a house. The company gives Chris the following guidelines for quoting on jobs such as this. 1. Calculate labour at \$95 per hour (this ﬁgure includes use of all tools and equipment). 2. Estimate the cost of materials delivered. 3. Find the total cost. 4. Add 15% as the company’s margin. 5. Add 10% GST. Chris makes the following notes when he goes to the site to give the customer a quote for this work 1 What should Creative Constructions quote for this work? 2 What amount should Creative Constructions give the government as the GST on this work? 3 Different trades and companies will have different procedures for quoting on work such as this. If there are students in the class whose families are involved in the building industry, ﬁnd out how they prepare quotations for work. inv estigat ioninv estigat ion Labour Remove existing wall — 2 builders @ 2 hours Foundations — 2 builders @ 14 hours Framework — 2 builders @ 24 hours Roof — 2 builders @ 8 hours Interior ﬁtting and ﬁnishing — 4 builders @ 16 hours Materials Concrete — \$600 Timber — \$4500 Tiles — \$2300 Windows/doors — \$1200 Mouldings etc. — \$800 Electricals — \$1100 MQ Maths A Yr 11 - 01 Page 19 Friday, July 6, 2001 8:30 AM
20. 20. 20 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Working overtime Karla has a rough idea of what overtime means: you are paid more if you work long or irregular hours. However, she is not sure how it is calculated and how much extra she should be paid. Overtime is paid when a wage earner works more than the regular hours each week. When an employee works overtime a higher rate is paid. This higher rate of pay is called a penalty rate. The rate is normally calculated at either: 1. time and a half, which means that the person is paid 1 times the 1. usual rate of pay, or 2. double time, which means that the person is paid twice the 1. normal rate of pay. A person may also be paid these overtime rates for working at unfavourable times such as at night or during weekends. To calculate the hourly rate earned when working overtime we multiply the normal hourly rate by the overtime factor, which is 1 for time and a half and 2 for double time. To calculate the pay for a period of time worked at time and a half or double time we multiply the normal pay rate by the overtime factor (either 1 or 2) and then by the number of hours worked at that overtime rate. 1 2 --- 1 2 --- Gustavo is paid \$9.78 per hour in his job as a childcare worker. Calculate Gustavo’s hourly rate when he is being paid for overtime at time and a half. THINK WRITE Multiply \$9.78 (the normal hourly rate) by 1 (the overtime factor for time and a half). Time and a half rate = \$9.78 × 1 Time and a half rate = \$14.671 2 --- 1 2 --- 14WORKEDExample 1 2 --- Adrian works as a shop assistant and his normal rate of pay is \$12.84 per hour. Calculate the amount that Adrian earns for 6 hours work on Saturday, when he is paid time and a half. THINK WRITE Multiply \$12.84 (the normal pay rate) by 1 (the overtime factor) and by 6 (hours worked at time and a half). Pay = \$12.84 × 1 × 6 Pay = \$115.561 2 --- 1 2 --- 15WORKEDExample MQ Maths A Yr 11 - 01 Page 20 Friday, July 6, 2001 1:40 PM
21. 21. C h a p t e r 1 E a r n i n g m o n e y 21 When we need to calculate the total pay for a week that involves overtime we need to calculate the normal pay and then add the amount earned for any overtime. Some examples will have more than one overtime rate to consider and some will require you to work out how many hours have been worked at each rate. Natasha works as a waitress and is paid \$11.80 per hour for a 38-hour week. Calculate Natasha’s pay in a week where she works 5 hours at time and a half in addition to her regular hours. THINK WRITE Calculate Natasha’s normal pay. Normal pay = \$11.80 × 38 = \$448.40 Calculate Natasha’s pay for 5 hours at time and a half. Time and a half = \$11.80 × 1 × 5 = \$88.50 Add the normal pay and the time and a half pay together. Total pay = \$448.40 + \$88.50 = \$536.90 1 2 1 2 --- 3 16WORKEDExample Graeme is employed as a car assembly worker and is paid \$10.40 per hour for a 36-hour week. If Graeme works overtime, the ﬁrst 6 hours are paid at time and a half and the remainder at double time. Calculate Graeme’s pay in a week where he works 45 hours. THINK WRITE Calculate the number of hours overtime Graeme worked. Overtime = 45 − 36 Overtime = 9 hours Of these nine hours, calculate how much was at time and a half and how much was at double time. Time and a half = 6 hours Double time = 3 hours Calculate Graeme’s normal pay. Normal pay = \$10.40 × 36 Normal pay = \$374.40 Calculate what Graeme is paid for 6 hours at time and a half. Time and a half = \$10.40 × 1 × 6 Time and a half = \$93.60 Calculate what Graeme is paid for 3 hours at double time. Double time = \$10.40 × 2 × 3 Double time = \$62.40 Calculate Graeme’s total pay by adding the time and a half and double time payments to his normal pay. Total pay = \$374.40 + \$93.60 + \$62.40 Total pay = \$530.40 1 2 3 4 1 2 --- 5 6 17WORKEDExample MQ Maths A Yr 11 - 01 Page 21 Wednesday, July 4, 2001 2:17 PM
22. 22. 22 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Working overtime 1 Reece works in a restaurant and is paid a normal hourly rate of \$11.30. Calculate the amount Reece earns each hour when he is being paid time and a half. 2 Carmen works as a waitress and is paid \$11.42 per hour. Calculate Carmen’s rate per hour on a Sunday when she is paid double time. 3 Gareth works as a train driver and is normally paid \$11.48 per hour. For working on public holidays he is paid double time and a half (overtime factor = 2 ). Calculate Gareth’s hourly rate of pay on a public holiday. 4 Ben works in a hotel and is paid \$11.88 per hour. Calculate the total amount Ben will earn for an 8-hour shift on Saturday when he is paid at time and a half. 5 Taylor works as an usher at a concert venue. She is normally paid \$13.10 per hour. Calculate Taylor’s pay for 6 hours on Sunday when she is paid double time. 6 Copy and complete the table below. 7 Ernie works as a chef and is paid \$9.95 per hour. What will Ernie’s hourly rate be when he is paid time and a half for overtime? A \$11.45 B \$14.92 C \$14.93 D \$19.90 Name Ordinary rate Overtime rate Hours worked Pay A. Nguyen \$8.90 Time and a half 4 M. Donnell \$9.35 Double time 6 F. Milo \$11.56 Time and a half 7 J. Carides \$13.86 Time and a half 6.5 Y. Robinson \$22.60 Double time 5.5 remember 1. Overtime is paid when you work more than your normal working hours in a week, and you receive a higher rate of pay for the extra hours. 2. Overtime can be paid at: (a) time and a half — 1 times the normal hourly rate (b) double time — twice the normal hourly rate. 3. To calculate the hourly rate when working overtime, multiply the normal hourly rate by the overtime factor. 4. To calculate the pay that is received for overtime, multiply the normal hourly rate by the overtime factor by the number of hours worked at that overtime rate. 5. To calculate the total pay for a week when overtime has been worked, calculate the normal pay and the pay for each overtime rate separately, and add them. 1 2 --- remember 1E WORKED Example 14 1 2 --- WORKED Example 15 mmultiple choiceultiple choice MQ Maths A Yr 11 - 01 Page 22 Wednesday, July 4, 2001 2:17 PM
23. 23. C h a p t e r 1 E a r n i n g m o n e y 23 8 Stephanie works in a shop and is paid \$9.40 per hour. Calculate how much more Steph- anie will earn in 8 hours work at time and a half than she would at ordinary rates. A \$37.60 B \$75.20 C \$112.80 D \$188.00 9 Eric works on the wharves unloading containers. Eric is paid \$14.20 per hour. Calcu- late the number of hours at time and a half that Eric will have to work to earn the same amount of money that he will earn in 9 hours at ordinary rates. A 4.5 hours B 6 hours C 10.5 hours D 13.5 hours 10 Rick works 37 hours at ordinary time each week and receives \$12.64 per hour. Calculate Rick’s pay in a week where, in addition to his normal hours, he works 4 hours overtime at time and a half. 11 Kirsty works 36 hours each week at a rate of pay of \$16.40 per hour. Calculate Kirsty’s pay in a week where, in addition to her ordinary hours, she works 4 hours on Sunday, when she is paid double time. 12 Grant works as a courier and is paid \$13.25 per hour for a 35-hour working week. Calculate Grant’s pay for a week where he works 4 hours at time and a half and 2 hours at double time in addition to his regular hours. 13 Copy and complete the table below. 14 Jenny is a casual worker at a motel. The normal rate of pay is \$10.40 per hour. Jenny works 8 hours on Saturday for which she is paid time and a half. On Sunday she works 6 hours for which she is paid double time. Jenny’s pay is equivalent to how many hours work at the normal rate of pay? A 14 B 21 C 24 D 28 15 Patricia works a 35-hour week and is paid \$14.15 per hour. Any overtime that Patricia does is paid at time and a half. Patricia wants to work enough overtime so that she earns more than \$600 each week. What is the minimum number of hours that Patricia will need to work to earn this amount of money? A 40 B 41 C 42 D 43 16 Steven works on a car assembly line and is paid \$12.40 per hour for a 36-hour working week. The ﬁrst 4 hours overtime he works each week is paid at time and a half with the rest paid at double time. Calculate Steven’s earnings for a week in which he works 43 hours. Name Ordinary rate Normal hours Time and a half hours Double time hours Total pay W. Clark \$8.60 38.5 4 — A. Hurst \$9.85 37.5 — 6.5 S. Gannon \$14.50 38.5 5 2.5 G. Dymock \$16.23 37.5 4 1.5 D. Colley \$24.90 36.5 6 8.5 mmultiple choiceultiple choice mmultiple choiceultiple choice WORKED Example 16 mmultiple choiceultiple choice mmultiple choiceultiple choice WORKED Example 17 MQ Maths A Yr 11 - 01 Page 23 Wednesday, July 4, 2001 2:17 PM