Question

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?

Answer 1

14 doctors

Explanation:

A chart is the easiest way to understand this question.

`color(white)(aaaaaaaa)`ratios`color(white)(aaa)`actual value
nurses`color(white)(aaia)`9`color(white)(aaaaaaa)`?
doctors`color(white)(aaa)`2`color(white)(aaaaiiaa)`?
Total`color(white)(aaaaa)`11`color(white)(aaaaaaa)`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.