Donna M got 34 questions on a quiz correct. She got 85% of the questions correct. How many questions were there on the quiz?

Jan 11, 2017

There were 40 questions on the quiz.

Explanation:

We can rewrite this as: 85% of what is 34?

"Percent" or "%" means "out of 100" or "per 100", Therefore 85% can be written as $\frac{85}{100}$.

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the number of questions we are looking for "q".

Putting this altogether we can write this equation and solve for $q$ while keeping the equation balanced:

$\frac{85}{100} \times q = 34$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{85}} \times \frac{85}{100} \times q = \frac{\textcolor{red}{100}}{\textcolor{b l u e}{85}} \times 34$

$\frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{85}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{85}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} \times q = \frac{3400}{\textcolor{b l u e}{85}}$

$q = 40$