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# Unit 1 Algebra and percentage

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### Unit 1 Algebra and percentage

1. 1. Algebra Unit #1 --- 2-1 R&A Algebra Chapter 2 PowerPoint Presentation Prepared by ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved C Quinn, Seneca College.
2. 2. Algebra Unit #1 --- 2-2 Algebra R&A Formula Manipulation Both sides of the equation must be treated in exactly the same way! You can add the same number to both sides You can subtract the same number from both sides You can multiply or divide both sides by the same number or variable You can raise both sides to the same exponent ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
3. 3. Algebra Unit #1 --- 2-3 Algebra R&A LO 2. Substitution Equation 6.1 P = \$100 principal amount Amount of interest Evaluate I = Prt r = 0.09 t = 7/12 7 Months rate of time in interest years I = \$100 * 0.09 * (7/12) I = \$100 * 0.0525 I = \$5.25 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Think 5.25 Use Calculator BEDM AS
4. 4. Algebra Unit #1 --- 2-4 Algebra R&A LO 2. Substitution Equation 6.2 P = \$100 Total Amount r = 0.09 t = 7/12 7 Months S = \$100 [1 + 0.09*(7/12)] S = \$100[1.0525] S = \$105.25 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved S = P(1 + rt) Think 105.25 Use Calculator BEDMAS
5. 5. Algebra Unit #1 --- 2-5 Algebra R&A LO 2. Formula Manipulation Example S = \$105.25 Evaluate S = P(1 + rt) P = \$100 r = 0.09 t = ? We must solve for t OR First substitute the numerical values given, and then manipulate the equation to solve for t ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved First rearrange the formula to isolate t, and then substitute the given numerical values give.
6. 6. Algebra Unit #1 --- 2-6 Algebra R&A Formula Manipulation LO 2. Example Evaluate S = P(1 + rt) First rearrange the formula to isolate t, and then substitute the given numerical values give. Multiply through by P S = P(1 + rt) S = P + Prt Subtract P from both sides S - P = Prt (S – P) / Pr = Prt/Pr Divide both sides by Pr (S – P) / Pr = t Now substitute ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
7. 7. Algebra Unit #1 --- 2-7 Algebra R&A LO 2. Formula Manipulation Example continued…. t = (S-P) / Pr S = \$105.25 P = \$100 r = 0.09 Now substitute t = (105.25 -100) / 100*0.09 t = .5833 years t = 7 months ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Multiply by 12 to change years to months
8. 8. Algebra 2-8 R&A LO 5. ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
9. 9. Algebra Unit #1 --- 2-9 R&A Base Method Formula % change = Final Value – Initial Value Initial Value c = Vf – Vi * 100% Vi ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
10. 10. Algebra Unit #1 --- 2-10 Algebra R&A Monday’s Sales were \$1000 and Tuesday’s were \$2500. Find the percent change. \$ % (/100) Initial Value 1000 100 1 250 Final Value 2500 2.5 Change 1500 150 1.5 x 100% = 2500 150% Increase 1000 Cross - multiply X = 2500*100% / 1000 = ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 250% …Alternate solution
11. 11. Algebra Unit #1 --- 2-11 R&A Monday’s Sales were \$1000 and Tuesday’s were \$2500. Find the percent change. This method is referred to as the Base Method % change = Difference Base c = Vf – Vi * 100% Vi ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Initial(Base)Value Final Value \$ 1000 2500 Difference \$ 1500 \$ 1500 % change = \$ 1000 = 1.5 or 150% Increase
12. 12. Algebra Unit #1 --- 2-12 R&A In the making of dried fruit, 15kg. of fruit shrinks to 3 kg. Find the percent change. Initial(Base)Value Final Value 15 3 % change = Difference Difference Base 12 c = Vf – Vi * 100% % change = 15 Vi 12 = .8 or 80% Decrease ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved …Alternate solution
13. 13. Algebra Unit #1 --- 2-13 R&A In the making of dried fruit, 15kg. of fruit shrinks to 3 kg. Find the percent change. Kg. Initial Value Final Value Difference x 100% = 3 % 15 3 12 100 20 80 (/100) 1 .2 .8 Cross - multiply 15 X = 3*100% / 15 = 20% ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 80% Decrease
14. 14. Algebra Unit #1 --- 2-14 R&A A chartered bank is lowering the interest rate on its loans from 9% to 7%. What will be the percent decrease in the interest rate on a given balance? % change = Difference Base = .07 - .09 = -.02 .09 .09 - = .2222 or 22.22% Decrease Increase in Interest Rate ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
15. 15. Algebra Unit #1 --- 2-15 R&A A chartered bank is increasing the interest rate on its loans from 7% to 9% What will be the percent increase in the interest rate on a given balance? % change = Difference Base = .09 - .07 = .02 .07 .07 =.2857 or 28.57% Increase ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
16. 16. Algebra Unit #1 --- 2-16 R&A You paid \$51.75 for a meal in Ontario which includes the taxes of 14%. What was the price of the meal prior to the addition of the taxes? Initial value = Final value 1 + % change = 51.75 = 1+ .14 =\$45.39 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 51.75 1.14
17. 17. Algebra Unit #1 --- 2-17 R&A You paid \$75 for a new coat after a 20% discount. What was the original price of the coat? Initial value = Final value 1 - % change Here the change is negative = 75.00 = 1 - .20 =\$93.75 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 75.00 .80