Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

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

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Percents can be used to describe a change. Percent of change is the ratio of the amount of change to the original amount.

Percent of increase describes how much the original amount increases.

Percent of decrease describes how much the original amount decreases.

amount of changeoriginal amountpercent of change =

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Find the percent of increase or decrease from 16 to 12.

Additional Example 1A: Finding Percent of Increase or Decrease

This is a percent of decrease.

16 – 12 = 4 First find the amount of change.

amount of decrease

original amount4

16Set up the ratio.

Find the decimal form. Write as a percent.

= 0.25 = 25% 416

From 16 to 12 is a 25% decrease.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and 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

945

Set up the ratio.

Additional Example 1B: Finding Percent of Increase or Decrease

Find the decimal form. Write as a percent.

= 0.20 = 20%945

From 45 to 54 is a 20% increase.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Find the percent increase or decrease from 50 to 65.

This is a percent of increase.

Check It Out! Example 1A

65 – 50 = 15 First find the amount of change.

amount of increase original amount

15 50

Set up the ratio.

Find the decimal form. Write as a percent.

= 0.30 = 30%15 50

From 50 to 65 is a 30% increase.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Find the percent of increase or decrease from 20 to 17.

Check It Out! Example 1B

This is a percent of decrease.

20 – 17 = 3 First find the amount of change.

amount of decrease

original amount3

20Set up the ratio.

Find the decimal form. Write as a percent.

= 0.15 = 15% 320

From 20 to 17 is a 15% decrease.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

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?

Additional Example 2: Health Application

26 72

Set up the ratio.

98 – 72 = 26 First find the amount of change.

amount of increase original amount

Find the decimal form. Write as a percent.

0.361 36.1%26 72

From 72 to 98 increases by about 36.1%.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

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?

Check It Out! Example 2

1.25 – 0.85 = 0.40 First find the amount of change.

amount of decreaseoriginal amount 1.25

0.40Set up the ratio.

Find the decimal form. Write as a percent.= 0.32 = 32%

1.25 0.40

The value of the stock decreased by 32%.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

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.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the discounted price?

Additional Example 3A: Finding Discount and Markup

(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.

Method 1: Multiply, then subtract.

(450)(0.80) = 360 Find 80% of 450.

The discounted price was $360.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Additional Example 3B: Finding Discount and Markup

(85)(0.40) = 34 Find 40% of $85. This is the amount of markup.

85 + 34 = 119 Add $34 to $85.Method 2: Add, then multiply.

100% + 40% = 140% Find the total percent of the selling price.

Method 1: Multiply, then add.

(85)(1.40) = 119 Find 140% of 85.

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?

The retail price is $119.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Check It Out! Example 3A

(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.

Method 1: Multiply, then subtract.

(750)(0.90) = 675 Find 90% of 750.

Lily bought a dog house originally priced at $750 that was on sale for 10% off. What was the sale price?

The sale price was $675.

Evaluating Algebraic Expressions

6-5 Applying Percent of Increase and Decrease

Check It Out! Example 3B

(30)(0.50)= 15 Find 50% of $30. This is the amount of markup.

30 + 15 = 45 Add $15 to $30.Method 2: Add, then multiply.100% + 50% = 150% Find the total percent of the

selling price.

Method 1: Multiply, then add.

(30)(1.50) = 45 Find 150% of 30.

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?

The retail price is $45.