# Donnovan earned 99 points on his science project. If his grade was a 90%, how many points were possible?

Nov 16, 2016

There were 110 possible points.

#### Explanation:

This problem could be rephrased as "99 is 90% of what number?".

One way to set it up is to use "is over of equals percent over 100".

$\frac{\text{is"/"of" = "%}}{100}$

$\frac{99}{x} = \frac{90}{100}$

Cross multiply.

$90 x = 99 \left(100\right)$

$90 x = 9900$

$\frac{90 x}{90} = \frac{9900}{90} \textcolor{w h i t e}{a a a}$

$x = 110$

A second way to think about the problem is "90% of x is 99#.
"Of" indicates multiplication and "is" means equal.

Convert 90% to the decimal .90 by dividing 90 by 100.

$.90 x = 99$

$\frac{.90 x}{.90} = \frac{99}{.90}$

$x = 110$