A hospital employs a total of 77 nurses and doctors. The ratio of nurses to doctors is 9:2. How many nurses are employed at the hospital? How many doctors are employed at the hospital?

Jan 12, 2017

14 doctors

Explanation:

A chart is the easiest way to understand this question.

$\textcolor{w h i t e}{a a a a a a a a}$ratios$\textcolor{w h i t e}{a a a}$actual value
nurses$\textcolor{w h i t e}{a a i a}$9$\textcolor{w h i t e}{a a a a a a a}$?
doctors$\textcolor{w h i t e}{a a a}$2$\textcolor{w h i t e}{a a a a i i a a}$?
Total$\textcolor{w h i t e}{a a a a a}$11$\textcolor{w h i t e}{a a a a a a a}$77

Since in the row labeled "Total" to move from column 1 to column 2 we would multiply the 11 by 7, so for each of the other rows.

Multiply the 9 by 7 to get 63 nurses, and multiply the 2 by 7 to get 14 doctors. Notice the total of nurses and doctors is $63 + 14 = 77$.
Therefore there are 14 doctors.