Lesson 8: Percent Increase and Decrease with Equations

Percent Increase and Decrease with Equations

Student Summary

We can use equations to express percent increase and percent decrease.

For example, if $y$ is 15% more than $x$ , we can represent this by using any of these equations:

$y = x + 0.15x$

$y = (1 + 0.15)x$

$y = 1.15x$

Tape diagram, entire length labeled 1.15x. Blue shaded portion labeled x. White portion labeled 0.15x.

So if someone makes an investment of $x$ dollars, and its value increases by 15% to reach $1,250, then we can write the equation $1.15x =1,250$ to find the value of the initial investment.

Here is another example: if $a$ is 7% less than $b$ , we can represent this by using any of these equations:

$a = b - 0.07b$

$a = (1-0.07)b$

$a = 0.93b$

Tape diagram, b labels the entire tape. Blue shaded portion, labeled 0.93b. White portion, labeled 0.07b.

So if the amount of water in a tank decreased 7% from its starting value of $b$ to its ending value of 348 gallons, then we can write $0.93b = 348$ .

Often, an equation is the most efficient way to solve a problem involving percent increase or percent decrease.

Visual / Anchor Chart

Standards

Building On

5.NF.B

No additional information available.

Addressing

7.EE.2

Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related.

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.