~ 4.12 ~

Learning Targets

• I can find the percentage increase or decrease when I know the original amount and the new amount.

To find a 30% increase over 50, we can find 130% of 50.

1.3 ⋅ 50 = 65

To find a 30% decrease from 50, we can find 70% of 50.

0.7 ⋅ 50 = 35

If we know the initial amount and the final amount, we can also find the percent increase or percent decrease. For example, a plant was 12 inches tall and grew to be 15 inches tall. What percent increase is this? Here are two ways to solve this problem:

• The plant grew 3 inches, because 15 − 12 = 3. We can divide this growth by the original height, 3 ÷ 12 = 0.25. So the height of the plant increased by 25%.

• The plant's new height is 125% of the original height, because 15 ÷ 12 = 1.25. This means the height increased by 25%, because 125 − 100 = 25.

Here are two ways to solve the problem: A rope was 2.4 meters long. Someone cut it down to 1.9 meters. What percent decrease is this?

• The rope is now 2.4 − 1.9, or 0.5 meters shorter. We can divide this decrease by the original length, 0.5 ÷ 2.4 = 0.2083333... So the length of the rope decreased by approximately 20.8%.

• The rope's new length is about 79.2% of the original length, because 1.9÷2.4=0.7916666... The length decreased by approximately 20.8%, because 100 − 79.2 = 20.8.

1. A salesperson sold a car for $18,250 and their commission is $693.50. What percentage of the sale price is their commission?

2. The bill for a meal was $33.75. The customer left $40.00. What percentage of the bill was the tip?

3. The original price of a bicycle was $375. Now it is on sale for $295. What percentage of the original price was the markdown?

With a coupon, you can get a pair of shoes that normally costs $84 for only $72. What percentage was the discount?

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