The document provides an agenda for a Friday class including warm-up exercises on percent of change and percent mark-up/discount, assignments due, and test reminders. It also includes sample math problems working through calculating percentages, percent increases and decreases, discounts, markups, and using proportions to solve for unknown values related to percentage word problems.

1. TGIF December 6, 2013
Today:
 Warm-Up
 Percent of Change
 Percent Mark-Up/Discount
 Complete all Class Work from this Week
 Reminders: Test Wednesday, Progress Reports
Thursday, Khan due by Sunday on-line,
Tuesday off-line

2. 1. What is 45% of 120?
You are 15 years old and have lived 16% of your life.
At what age will you die?(Round to nearest year)
3. 36 is what % of 30? 4. 48 is 300% of what number?
4. Try using mental math first: 1) 25% of 80
2) 120% of 50 3) 15% of 500
5) 5% of 1500
4) 300% of 9
6) What % of 35 is 7?

3. You have $100 and are playing poker. You lose 50% of your
money in the first hand. In the second hand, you bet
everything and win 50% of your money back. How much
money do you have now?

4. Vocabulary & Formulas
Section of Notebook

5. Vocabulary & Formulas:
Finding Percent Increase & Decrease
 A percent change is an increase or
decrease given as a percent of the original
amount. Percent increase describes an
amount that has grown and percent
decrease describes an amount that has be
reduced.

6. Vocabulary & Formulas:
Finding Price Before Increase or Decrease
 This formula is used to find the original price of an item
when the price is known after increases such as taxes, tips,
and markups.
 The formula is also used when the original price is not
known after decreases such as markdowns and discounts.
Original Price:
Price after increase or decrease
1 + percent or
The cost of lunch after a 15% tip was $24.15. What was the
cost of the lunch alone? $24.15
1.15 1 +15%
= $21.00

7. Applying Percent Changes
Common percent changes are discounts and
markups.
A discount is an
original price
discount
= % of
amount by which an
– discount
final price = original price
original price is
reduced.
A markup is an
markup
= % of wholesale cost
amount by which a
wholesale price is final price = wholesale cost
increased.
+ markup

8. Class Notes & Practice Problems:

9. Ex. 1A: Percent Increase and Decrease
Find each percent change. Tell whether it is a
percent increase or decrease. 10
From 8 to
Simplify the fraction.
= 0.25
= 25%
Change to a decimal.
Write the answer as a percent.
8 to 10 is an increase, so a change from 8 to 10 is a 25%
increase.

10. Ex. 1B: Finding Percent Increase and Decrease
Find the percent change. Tell whether it is a percent
increase or decrease. From 75 to 30
Simplify the fraction.
Simplify the numerator.
Write as a decimal
= 0.6
Write the answer as a percent.
= 60%
75 to 30 is a decrease, so a change from 75 to 30 is a
60% decrease.

11. Practice 1: Percent Increase and Decrease
Find the percent change. Tell whether it is a percent
increase or decrease.
1. From 200 to 110
Simplify the numerator.
Simplify the fraction.
Write as a decimal
= 0.45
= 45%
Write the answer as a percent.
200 to 110 is an decrease, so a
change from 200 to 110 is a 45%
decrease.

12. Practice 2: Percent Increase and Decrease
Find each percent change. Tell whether it is a
percent increase or decrease.
2. From 25 to 30
Simplify the numerator.
Simplify the fraction.
= 0.20
= 20%
Write as a decimal
Write the answer as a percent.
25 to 30 is an increase, so a change from 25 to
30 is a 20% increase.

13. Example 1: Percent Increase and Decrease
A. Find the result when 12 is increased by 50%.
Find 50% of 12. This is the amount of
increase.
It is a percent increase, so add 6
12 + 6 =18
to the
12 increased by 50% isoriginal amount.
18.
0.50(12) = 6
B. Find the result when 55 is decreased by
60%.
0.60(55) = 33 Find 60% of 55. This is the amount of decrease.
55 – 33 = 22
It is a percent decrease so subtract 33 from
the original amount.
55 decreased by 60% is 22.

14. Example 2: Percent Increase and Decrease
A. Find the result when 72 is increased by 25%.
0.25(72) = 18 Find 25% of 72. This is the amount of
72 + 18 =90
increase.
It is a percent increase, so add 18
to the original amount.
72 increased by 25% is 90.
B. Find the result when 10 is decreased
by 40%.
Find 40% of 10. This is the amount of
0.40(10) = 4
decrease.
It is a percent decrease so subtract 4
10 – 4 = 6
from the original amount.
10 decreased by 40% is 6.

15. Applying Percent Changes
Common percent changes are discounts and
markups.
A discount is an
original price
discount
= % of
amount by which an
– discount
final price = original price
original price is
reduced.
A markup is an
markup
= % of wholesale cost
amount by which a
wholesale price is final price = wholesale cost
increased.
+ markup

16. Practice 1: Percent Discounts
The entrance fee at an amusement park is $35.
People over the age of 65 receive a 20% discount.
What is the amount of the discount? How much do
people over 65 pay?
Method 1: A discount is a percent decrease. So find
$35 decreased by 20%.
0.20(35) = 7
35 – 7 = 28
Find 20% of 35. This is the
amount of the discount.
Subtract 7 from 35. This is the
entrance fee for people over
the age of 65.

17. Practice 2: Percent Discounts
Method 2: Subtract the percent discount from
100%.
100% – 20% = 80%
0.80(35) = 28
35 – 28 = 7
People over the age of 65 pay 80% of
the regular price, $35.
Find 80% of 35. This is the entrance
fee for people over the age of 65.
Subtract 28 from 35. This is the
amount of the discount.
By either method, the discount is $7. People over the
age of 65 pay $28.00.

18. Practice 3: Percent Discounts
A $220 bicycle was on sale for 60% off. Find the sale
price.
Use Method 2:
100% – 60% = 40%
0.40(220) = 88
The bicycle was 60% off of 100% .
Find 40% of 220.
By this method, the sale price is
$88.

19. Practice 1: Percent Markups
The wholesale cost of a DVD is $7. The markup is
85%. What is the amount of the markup? What is the
selling price?
Method 2
Method 1
A markup is a percent increase. 100%
Add percent markup to So find $7 increased by 85%.
100% + 85% = 185%
0.85(7) = 5.95
7 + 5.95 12.95
1.85(7)== 12.95
12.95 ÷ 7 = 5.95
Find 85% of 7. This is the amount of the
The selling price is 185% of the
markup.
wholesale price, 7.
Add to 7. This This is the selling
Find 185% of 7.is the selling price. price.
Subtract from 12.95. This is the
amount of the markup.
By either method, the amount of the markup is
$5.95. The selling price is $12.95.

20. Practice 2: Percent Markups
A video game has a 70% markup. The wholesale cost
is $9. What is the selling price?
Method 1
A markup is a percent increase. So find $9 increased
by 70%.
0.70(9) = 6.30
9 + 6.30 = 15.30
Find 70% of 9. This is the amount of
the markup.
Add to 9. This is the selling price.
The amount of the markup is $6.30. The selling price is
$15.30.

21. Lesson Quiz: Part I
Find each percent change. Tell whether it is a
percent increase or decrease.
1. from 20 to 28. 40% increase
2. from 80 to 62. 22.5% decrease
3. from 500 to 100.80% decrease
4. find the result when 120 is increased by 40%. 168
5. find the result when 70 is decreased by 20%. 56

22. Lesson Quiz: Part II
Find each percent change. Tell whether it is a percent
increase or decrease.
6. A movie ticket costs $9. On Mondays, tickets are
20% off. What is the amount of discount? How
much would a ticket cost on a Monday? $1.80; $7.20
7. A bike helmet cost $24. The wholesale cost was
$15. What was the percent of markup? 60%

23. Example 2: Measurement Application
A flagpole casts a shadow that is 75 ft long at the
same time a 6-foot-tall man casts a shadow that is 9 ft
long. Write and solve a proportion to find the height
of the flag pole.
Since h is multiplied by 9, divide both sides
by 9 to undo the multiplication.
The flagpole is 50 feet tall.

26. Percents
Warm Up What is 70% of ½?
Change each percent to a decimal.
1. 73% 0.73
2. 112% 1.12
3. 0.6% 0.006
4. 1%
0.01
Change each fraction or mixed number to a
decimal.
5.
0.5
6.
0.3
7.
0.8
8.
Solve each proportion.
9.
12
10.
4.2
1.2

27. Percents
Example 3B: Finding the Whole
20 is 0.4% of what number?
Method 2 Use an equation.
20 = 0.4% of x
20 = 0.004
•
x
5000 = x
20 is 0.4% of 5000.
Write an equation. Let x represent
the whole.
Write the percent as a decimal.
Since x is multiplied by 0.004,
divide both sides by 0.004 to
undo the multiplication.

28. Percents
120% of what number is 90?
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
120x = 9000
x = 75
120% of 75 is 90.
Find the cross products.
Since x is multiplied by 120, divide
both sides by 120 to undo the
multiplication.

29. Percents
Lesson Quiz: Part 1
Find each value. Round to the nearest tenth
if necessary.
1. Find 20% of 80.
16
2. What percent of 160 is 20? 12.5%
3. 35% of what number is 40? 114.3
4. 120 is what percent of 80?
5. Find 320% of 8.
150%
25.6
6. 65 is 0.5% of what number?
13,000

30. Warm-Up:
1. Order from least to greatest: 2/8, 2.8%, 8/2, .28
3. 20 is 40% of what number?
4. 36 is what percent of 30?
5. What is the total cost of a $21.00 lunch and 15%
tip?
6. Which fraction must have more than two decimal
places?
A.) ¼ B.) 2/5
C.) 12/50 D.) 5/6
E.)
None

31. * A certain item used to sell for seventy-five cents a pound, you see that it's
been marked up to eighty-one cents a pound. What is the percent increase?
First, I have to find the increase: 81 – 75 = 6
The price has gone up six cents. Now I can find the percentage increase over the
original price.
Note this language, "increase/decrease over the original", and use it to your
advantage: it will remind you to put the increase or decrease over the original value,
and then divide.
This percentage increase is the relative change:
6/75 = 0.08
or an 8% increase in price per pound.
An important category of percentage exercises is markup and markdown problems.
For these, you calculate the markup or markdown in absolute terms (you find by how
much the quantity changed), and then you calculate the percent change relative to
the original value. So they're really just another form of "increase - decrease"
exercises.
* A computer software retailer used a markup rate of 40%. Find the selling
price of a computer game that cost the retailer $25.
The markup is 40% of the $25 cost, so the markup is: (0.40)(25) = 10

32. * A golf shop pays its wholesaler $40 for a certain club, and then sells it to a
golfer for $75. What is the markup rate?
First, I'll calculate the markup in absolute terms:
75 – 40 = 35
Then I'll find the relative markup over the original price, or the markup rate: ($35) is
(some percent) of ($40), or: Copyright © Elizabeth Stapel 1999-2009 All Rights
Reserved
35 = (x)(40)
so the relative markup over the original price is:
35 ˜ 40 = x = 0.875
Since x stands for a percentage, I need to remember to convert this decimal value to
the corresponding percentage.The markup rate is 87.5%.
* A shoe store uses a 40% markup on cost. Find the cost of a pair of shoes that
sells for $63.
This problem is somewhat backwards. We have the selling price, which is cost plus
markup, and they gave me the markup rate, but they didn't tell me the actual cost or
markup. So I have to be clever to solve this.
I will let "x" be the cost. Then the markup, being 40% of the cost, is 0.40x. And the
selling price of $63 is the sum of the cost and markup, so:
63 = x + 0.40x
63 = 1x + 0.40x
63 = 1.40x
63 ˜ 1.40 = x= 45

33. * An item originally priced at $55 is marked 25% off. What is the sale price?
First, find the markdown. The markdown is 25% of the price of $55, so:
x = (0.25)(55) = 13.75
By subtracting this markdown from the original price, find the sale price:
55 – 13.75 = 41.25
The sale price is $41.25.
* An item that regularly sells for $425 is marked down to $318.75. What is the
discount rate?
First, I'll find the amount of the markdown:
425 – 318.75 = 106.25
Then I'll calculate "the markdown over the original price", or the markdown rate:
($106.25) is (some percent) of ($425), so: 106.25 = (x)(425)
...and the relative markdown over the original price is:
x = 106.25 ˜ 425 = 0.25
Since the "x" stands for a percentage, I need to remember to convert this decimal
to percentage form. The markdown rate is 25%.

34. * An item is marked down 15%; the sale price is $127.46. What was the original
price?
This problem is backwards. They gave me the sale price ($127.46) and the
markdown rate (15%), but neither the markdown amount nor the original price. I will let
"x" stand for the original price. Then the markdown, being 15% of this price, was 0.15x.
And the sale price is the original price, less the markdown, so I get: x – 0.15x = 127.46
1x – 0.15x = 127.46
0.85x = 127.46
x = 127.46 ˜ 0.85 = 149.952941176...
This problem didn't state how to round the final answer, but dollars-and-cents is
always written with two decimal places, so: The original price was $149.95.
Note in this last problem that I ended up, in the third line of calculations, with an equation
that said "eighty-five percent of the original price is $127.46". You can save yourself
some time if you think of discounts in this way: if the price is 15% off, then you're only
actually paying 85%. Similarly, if the price is 25% off, then you're paying 75%; if the price
is 30% off, then you're paying 70%; and so on.
While the values below do not refer to money, the procedures used to solve these
problems are otherwise identical to the markup - markdown examples on the previous
page.
* Your friend diets and goes from 125 pounds to 110 pounds. What was her
percentage weight loss?
First, I'll find the absolute weight loss:
125 – 110 = 15
This fifteen-pound decrease is some percentage of the original, since the rate of
change is always with respect to the original value. So the percentage is "change over