Let's solve the problem step-by-step:
1. Understand the given ratio:
- The ratio of candidates interviewed to offers made is [tex]\(3:2\)[/tex]. This means for every 3 candidates interviewed, 2 offers are made.
2. Identify the target:
- We need to find how many applicants need to be interviewed to make 50 offers.
3. Set up the ratio in terms of offers:
- Since the ratio of interviewed candidates to offers made is [tex]\(3:2\)[/tex], we can represent this relationship mathematically as:
[tex]\[
\frac{\text{interviewed}}{\text{offers}} = \frac{3}{2}
\][/tex]
- Let's denote the number of candidates interviewed as [tex]\( x \)[/tex].
4. Set up the proportion:
- According to the ratio, for every 2 offers, 3 candidates are interviewed. Therefore, to maintain this ratio for 50 offers, we set up the following proportion:
[tex]\[
\frac{x}{50} = \frac{3}{2}
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], we can cross multiply:
[tex]\[
x \cdot 2 = 50 \cdot 3
\][/tex]
- Simplify the equation:
[tex]\[
2x = 150
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{150}{2} = 75
\][/tex]
Therefore, to make 50 offers, 75 applicants need to be interviewed. The correct answer is:
C. 75
