Question

dig deeper! 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? there are \\(\square\\) nurses and \\(\square\\) doctors.

Explanation:

Step1: Find the total parts of the ratio

The ratio of nurses to doctors is \(9:2\), so the total number of parts is \(9 + 2 = 11\) parts.

Step2: Find the value of one part

The total number of nurses and doctors is 77. So, the value of one part is \(77\div11 = 7\).

Step3: Calculate the number of nurses

Since the number of parts for nurses is 9, the number of nurses is \(9\times7 = 63\).

Step4: Calculate the number of doctors

Since the number of parts for doctors is 2, the number of doctors is \(2\times7 = 14\).

Answer:

There are \(\boldsymbol{63}\) nurses and \(\boldsymbol{14}\) doctors.