Question

If a certain town has 90 doctors and the ratio of male doctors to female doctors is 3 to 2, then the number of female doctors in this town is

• A. 18
• B. 30
• C. 36
• D. 45
• E. 54

Hint:

When you have a ratio (like a:b) and a total, think of the total as being made up of \(a+b\) "shares." Find the value of one share by dividing the total by \(a+b\), then multiply by \(a\) or \(b\) to find the size of each group.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a ratio problem. We are given the total number of individuals and the ratio between two subgroups. We need to find the actual number of individuals in one of the subgroups.
Step 2: Key Formula or Approach:
1. Add the parts of the ratio to find the total number of "ratio parts." 2. Divide the total number of individuals by the total number of ratio parts to find the value of one "part." 3. Multiply the value of one part by the number of parts corresponding to the desired subgroup.
Step 3: Detailed Explanation:
The ratio of male doctors to female doctors is 3:2. 1. Total ratio parts: The total number of parts in the ratio is \(3 + 2 = 5\). This means that for every 5 doctors, 3 are male and 2 are female. 2. Value of one part: The total number of doctors is 90. We divide the total by the number of parts to find out how many doctors are in each "part." \[ \text{Value of one part} = \frac{\text{Total doctors}}{\text{Total parts}} = \frac{90}{5} = 18 \] So, one "part" of the ratio represents 18 doctors. 3. Number of female doctors: The ratio for female doctors is 2 parts. \[ \text{Number of female doctors} = 2 \times (\text{Value of one part}) = 2 \times 18 = 36 \] As a check, the number of male doctors would be \(3 \times 18 = 54\). Total doctors = \(36 + 54 = 90\). This matches the given total.
Step 4: Final Answer:
There are 36 female doctors in the town.