Bellwork
1. Find 30% of 40.
12
2. Find 28% of 60.
16.8
Solve for x.
3. 22 = x(50)
0.44
4. 17.2 = x(86)
0.2
5. 20 is what percent of 80?
25%
6. 36 is what percent of 30?
120%
Percent Increase and
Percent Decrease
Objective
Find percent increase and 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.
Find each percent change. Tell whether it is a
percent increase or decrease.
From 8 to 10
Simplify the fraction.
Simplify the numerator.
= 0.25
Write the answer as a percent.
= 25%
8 to 10 is an increase, so a change from 8 to 10
is a 25% increase.
Helpful Hint
Before solving, decide what is a reasonable
answer. For Example 1A, 8 to 16 would be a
100% increase. So 8 to 10 should be much
less than 100%.
Find the percent change. Tell whether it is a
percent increase or decrease.
From 75 to 30
Simplify the fraction.
Simplify the numerator.
= 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.
Find each percent change. Tell whether it is a
percent increase or decrease.
From 200 to 110
Simplify
numerator.
Simplify
thethe
fraction.
= 0.45
Write the answer as a percent.
= 45%
200 to 110 is a decrease, so a change from 200
to 110 is a 45% decrease.
Find each percent change. Tell whether it is a
percent increase or decrease.
From 25 to 30
Simplifythe
thefraction.
numerator.
Simplify
= 0.20
Write the answer as a percent.
= 20%
25 to 30 is an increase, so a change from 25 to
30 is a 20% increase.
Find each percent change. Tell whether it is a
percent increase or decrease.
From 80 to 115
Simplifythe
thefraction.
numerator.
Simplify
= 0.4375
= 43.75% Write the answer as a percent.
80 to 115 is an increase, so a change from 80 to
115 is a 43.75% increase.
A. Find the result when 12 is increased by 50%.
0.50(12) = 6
12 + 6 =18
Find 50% of 12. This is the amount of
increase.
It is a percent increase, so add 6 to
the original amount.
12 increased by 50% is 18.
B. Find the result when 55 is decreased by 60%.
Find 60% of 55. This is the amount of
0.60(55) = 33
decrease.
It is a percent decrease so subtract
55 – 33 = 22
33 from the the original amount.
55 decreased by 60% is 22.
A. Find the result when 72 is increased by 25%.
0.25(72) = 18
Find 25% of 72. This is the amount of
increase.
72 + 18 =90
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.
Common application of percent change are discounts
and markups.
A discount is an
discount = % of original price
amount by which
an original price is final price = original price – discount
reduced.
A markup is an
markup = % of wholesale cost
amount by which
a wholesale cost final price = wholesale cost + markup
is increased.
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.
Method 2 Subtract the percent discount from
100%.
100% – 20% = 80%
People over the age of 65 pay
80% of the regular price, $35.
0.80(35) = 28
Find 80% of 35. This is the
entrance fee for people over
the age of 65.
35 – 28 = 7
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.
Helpful Hint
Before solving, decide what is a reasonable
answer. For example 3A, a 10% discount is $3.50
off. So a 20% discount would be more than $2
off.
A student paid $31.20 for art supplies that
normally cost $52.00. Find the percent
discount .
$52.00 – $31.20 = $20.80
Think: 20.80 is what
percent of 52.00? Let x
represent the percent.
The discount is 40%
A $220 bicycle was on sale for 60% off.
Find the sale price.
Method 2 Subtract the percent discount from
100%.
100% – 60% = 40%
0.40(220) = 88
220 – 88 = 142
The bicycle was 60% off of
100% .
Find 40% of 220. This is the
discount from the original
price.
By this method, the discount is $88. The sale price
is $142.00.
Ray paid $12 for a $15 T-shirt. What was
the percent discount ?
$15 – $12 = $3
The discount is 20%.
Think: 3 is what percent of
15? Let x represent the
percent.
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 markup to 100%
Add
percent
A markup is a percent increase. So find $7
The selling price is 185% of the
increased
by 85%.
100%
+ 85%
= 185% Find 85% of 7. This is the amount
wholesale price, 7.
0.85(7) = 5.95
of the markup.
Find 185% of 7. This is the selling
1.85(7) = 12.95
7 + 5.95 = 12.95
Add
to 7. This is the selling price.
price.
12.95  7 = 5.95
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.
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
Find 70% of 9. This is the amount
of the markup.
9 + 6.30 = 15.30
Add to 9. This is the selling price.
The amount of the markup is $6.30. The selling price
is $15.30.
What is the percent markup on a car selling for
$21,850 that had a wholesale cost of $9500?
21,850 – 9,500 = 12,350
Think: 12,350 is what percent of
9,500? Let x represent the
percent.
The markup was 130 percent.