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All courses Math Foundations · MF.RN.7 13 of 60
Calculate percent increase and decrease and explain what the percent measures.

Find a percent increase

Problem
A quantity increases from 40 to 50. What is the percent increase?
Your answer
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Hint

First find the increase: subtract the starting amount from the new amount, 50 - 40.

Percent increase compares the change to the original amount, so use 40 as the reference amount, not 50.

Solution walkthrough

01

Find how much the quantity increased

\[50~-~40~=~10\]

Percent increase starts with the change. The quantity went up by 10.

02

Compare the change to the starting amount

\[\frac{10}{40}~=~0.25\]

For percent increase, the change is measured against the original amount, which is 40, not the new amount 50.

03

Convert the decimal to a percent

\[0.25~=~25\%\]

A percent tells how many parts out of 100. Converting 0.25 to a percent gives 25%.

04

State the percent increase

\[\text{Percent increase}~=~25\%\]

The quantity increased by 25% because the increase of 10 is 25% of the original 40.

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Another way

  1. Check by using the percent on the original amount: 25% of 40 is 10, and 40 + 10 = 50, so 25% matches the increase.

!

Common mistake

A common mistake is dividing by the new amount: \(\frac{10}{50}=0.2=20\%\). That is wrong because percent increase must compare the change to the original amount, 40.