1. NS1.6 Calculate the percentage of increase and decrease of a quantity.
NS1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
California
Standards

2. Percents can be used to describe a change
Percents can be used to describe a change. Percent of change is the ratio of the amount of change to the original amount.
amount of change
original amount
percent of change =
Percent of increase describes how much the original amount increases.
Percent of decrease describes how much the original amount decreases.

3. Additional Example 1A: Finding Percent of Increase or Decrease
Find the percent of increase or decrease from 16 to 12.
This is a percent of decrease.
16 – 12 = 4 First find the amount of change.
amount of decrease
original amount 4 16
Set up the ratio. 4 16
Find the decimal form. Write as a percent.
= 0.25 = 25%
From 16 to 12 is a 25% decrease.

4. Additional Example 1B: Finding Percent of Increase or Decrease
Find the percent increase or decrease from 45 to 54.
This is a percent of increase.
54 – 45 = 9 First find the amount of change.
amount of increase
original amount 9 45
Set up the ratio. 9 45
= 0.20 = 20%
Find the decimal form. Write as a percent.
From 45 to 54 is a 20% increase.

5. Check It Out! Example 1A
Find the percent increase or decrease from 50 to 65.
This is a percent of increase.
65 – 50 = 15 First find the amount of change.
amount of increase
original amount 15 50
Set up the ratio. 15 50
= 0.30 = 30%
Find the decimal form. Write as a percent.
From 50 to 65 is a 30% increase.

6. Check It Out! Example 1B
Find the percent of increase or decrease from 20 to 17.
This is a percent of decrease.
20 – 17 = 3 First find the amount of change.
amount of decrease
original amount 3 20
Set up the ratio. 3 20
Find the decimal form. Write as a percent.
= 0.15 = 15%
From 20 to 17 is a 15% decrease.

7. Additional Example 2: Health Application
When Jim was exercising, his heart rate went from 72 beats per minute to 98 beats per minute. What was the percent increase to the nearest tenth of a percent?
98 – 72 = 26 First find the amount of change.
amount of increase
original amount 26 72
Set up the ratio. 26 72
  36.1%
Find the decimal form. Write as a percent.
From 72 to 98 increases by about 36.1%.

8. Check It Out! Example 2
In 2005, a certain stock was worth $1.25 a share. In 2006, the same stock was worth $0.85 a share. What was the percent decrease?
1.25 – 0.85 = First find the amount of change.
amount of decrease
original amount
1.25
0.40
Set up the ratio.
Find the decimal form. Write as a percent.
1.25
0.40
= 0.32 = 32%
The value of the stock decreased by 32%.

9. Discount is the difference between the regular price and the sale price of an item. You can use percent of decrease to find discounts.
Markup is the difference between the wholesale cost and the retail price of an item. You can use percent of increase to find markups.

10. Additional Example 3A: Finding Discount and Markup
Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the discounted price?
Method 1: Multiply, then subtract.
(450)(0.20) = 90 Find 20% of $450. This is the amount of discount.
450 – 90 = 360 Subtract $90 from $450.
Method 2: Subtract, then multiply.
100% – 20% = 80% Find the percent Sarah pays.
(450)(0.80) = 360 Find 80% of 450.
The discounted price was $360.

11. Additional Example 3B: Finding Discount and Markup
Mr. Olsen has a computer business in which he sells everything 40% above the wholesale price. If he purchased a printer for $85 wholesale, what will be the retail price?
Method 1: Multiply, then add.
(85)(0.40) = 34 Find 40% of $85. This is the amount of markup.
= Add $34 to $85.
Method 2: Add, then multiply.
100% + 40% = 140% Find the total percent of the selling price.
(85)(1.40) = 119 Find 140% of 85.
The retail price is $119.

12. Check It Out! Example 3A
Lily bought a dog house originally priced at $750 that was on sale for 10% off. What was the sale price?
Method 1: Multiply, then subtract.
(750)(0.10)= 75 Find 10% of $750. This is the amount of discount.
750 – 75 = 675 Subtract $75 from $750.
Method 2: Subtract, then multiply.
100% – 10% = 90% Find the percent Lily pays.
(750)(0.90) = 675 Find 90% of 750.
The sale price was $675.

13. Method 1: Multiply, then add.
Check It Out! Example 3B
Barb has a grocery store in which she sells everything at 50% above the wholesale price. If she purchased a prime rib for $30 wholesale, what will be the retail price?
Method 1: Multiply, then add.
(30)(0.50)= 15 Find 50% of $30. This is the amount of markup.
= Add $15 to $30.
Method 2: Add, then multiply.
100% + 50% = 150% Find the total percent of the selling price.
(30)(1.50) = 45 Find 150% of 30.
The retail price is $45.