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Percent of Increase and Decrease

When some quantity gets bigger or smaller, we can talk about the percent of increase or percent of decrease . Basically we are asking "what percent of the original quantity was added (or taken away)?"

First find the actual amount of the raise by finding the difference between the original salary and the new salary.

$2990-2600=390$

Now find what percent the $\$390$ raise is of the original salary of $\$2600$ . Write a proportion.

$\frac{390}{2600}=\frac{x}{100}$

Equate the cross products.

$2600x=39000$

Divide both sides by $2600$ .

$x=15$

So, Fauzia got a $15\%$ raise.

First, find the difference.

$200-135=65$

Now find what percent $65$ is of $200$ . Write a proportion.

$\frac{65}{200}=\frac{x}{100}$

Equate the cross products.

$6500=200x$

Divide both sides by $200$ .

$x=32.5$

So, the price was reduced by $32.5\%$ .

Another method is to find the amount of increase or decrease, write this as the numerator over the original amount, and then convert that fraction to a decimal.

First, find the difference.

$2.26-1.94=0.32$

Write this as the numerator of a fraction, over the original thickness.

$\frac{0.32}{2.26}$

Convert the fraction to a decimal. (Use a calculator.)

$\frac{0.32}{2.26}\approx 0.14$

So, the thickness decreased by about $14\%$ .