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?

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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?

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Answer 1 · 2017-01-12T18:20:05

14 doctors

Explanation:

A chart is the easiest way to understand this question.

$a a a a a a a a$ $color(white)(aaaaaaaa)$ ratios $a a a$ $color(white)(aaa)$ actual value
nurses $a a i a$ $color(white)(aaia)$ 9 $a a a a a a a$ $color(white)(aaaaaaa)$ ?
doctors $a a a$ $color(white)(aaa)$ 2 $a a a a i i a a$ $color(white)(aaaaiiaa)$ ?
Total $a a a a a$ $color(white)(aaaaa)$ 11 $a a a a a a a$ $color(white)(aaaaaaa)$ 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 $63 + 14 = 77$ $63+14=77$ .
Therefore there are 14 doctors.

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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?

1 Answer

Explanation:

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