Question

Two people quit work and begin college at the same time. Their salary and education information is given in the table below.

Salary prior to school
Years attending college
Total cost of college
Salary upon graduating
Person A
$18,000
3
$45000
$33,000
Person B
$27,000
4
$30,000
$37,000

Choose the true statement.
a.
Person A recovers their investment in a shorter amount of time.
b.
Person B recovers their investment in a shorter amount of time.
c.
They recover their investments in the same amount of time.
d.
There is too little information to compare the time to recover their investments.



Please select the best answer from the choices provided


A
B
C
D

Answer 1

To determine which person recovers their investment in education more quickly, we need to calculate the time it takes for each individual to make back their total investment in college through increased salary.

**Investment Recovery Time Calculation:**

1. **Person A:**
- Salary before college: $18,000
- Salary after college: $33,000
- Total cost of college: $45,000

**Net Gain in Salary:**
\[
\text{Net Gain} = \text{Salary after} - \text{Salary before} = 33,000 - 18,000 = 15,000
\]

**Time to Recover Investment:**
\[
\text{Time} = \frac{\text{Total Cost}}{\text{Net Gain per Year}} = \frac{45,000}{15,000} = 3 \text{ years}
\]

2. **Person B:**
- Salary before college: $27,000
- Salary after college: $37,000
- Total cost of college: $30,000

**Net Gain in Salary:**
\[
\text{Net Gain} = \text{Salary after} - \text{Salary before} = 37,000 - 27,000 = 10,000
\]

**Time to Recover Investment:**
\[
\text{Time} = \frac{\text{Total Cost}}{\text{Net Gain per Year}} = \frac{30,000}{10,000} = 3 \text{ years}
\]

**Comparison of Investment Recovery Time:**
Both Person A and Person B take **3 years** to recover their investments in college.

Therefore, the correct answer is:
**C. They recover their investments in the same amount of time.**