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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

Identify the percent-change base

\[\text{original}~=~40;~\text{new}~=~50\]

Percent increase is measured against the original amount, which is 40.

02

Find the increase

\[\text{change}~=~\text{new}~-~\text{original}~=~50~-~40~=~10\]

The quantity grew by 10 units.

03

Compare change with the original

\[\text{percent}~\text{increase}~=~\text{change}~/~\text{original}~=~10/40~=~1/4\]

Dividing the change by the starting amount gives the fractional increase.

04

Convert and check

\[1/4~=~0.25~=~25\%;~40~\times~1.25~=~50\]

A 25% increase adds one fourth of 40, and multiplying by 1.25 rebuilds the new amount.

05

State the percent increase

\[25\%\]

The quantity increased by 25% of its original value.

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Another way

  1. Notice that the increase 10 is one fourth of 40, and one fourth equals 25%.

!

Common mistake

Do not divide the change by the new amount 50. Percent increase uses the original amount 40 as its base.

Solution walkthrough video