Lesson 12: Solving Multi-step Percentage Problems

Solving Multi-step Percentage Problems

Student Summary

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

$1.3 \boldcdot 50 = 65$

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

$0.7 \boldcdot 50 = 35$

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: $3 \div 12 = 0.25$ . So the height of the plant increased by 25%.

The plant’s new height is 125% of the original height, because $15 \div 12=1.25$ . This means the height increased by 25%, because $125 - 100 = 25$ .

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

The rope is now $2.4 - 1.9$ , or 0.5, meter shorter. We can divide this decrease by the original length: $0.5 \div 2.4 = 0.208\overline3$ . 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 $1.9 \div 2.4 = 0.791\overline6$ . The length decreased by approximately 20.8%, because $100 - 79.2 = 20.8$ .

Visual / Anchor Chart

Standards

Building On

6.EE.2

Write, read, and evaluate expressions in which letters stand for numbers.

Addressing

7.RP.3

Use proportional relationships to solve multistep ratio and percent problems.

Building Toward

7.RP.3

Use proportional relationships to solve multistep ratio and percent problems.