To determine which person recovers their investment in education more quickly, we need to compare the time taken for each person to recoup their college expenses given their increase in salary upon graduation.
### Step-by-Step Solution:
1. Calculate the increase in salary upon graduating:
- For Person A:
- Salary Prior to College: [tex]$18,000
- Salary Upon Graduating: $[/tex]33,000
- Increase in Salary, [tex]\( \Delta \text{Salary}_A \)[/tex]: [tex]\( 33,000 - 18,000 = 15,000 \)[/tex]
- For Person B:
- Salary Prior to College: [tex]$27,000
- Salary Upon Graduating: $[/tex]37,000
- Increase in Salary, [tex]\( \Delta \text{Salary}_B \)[/tex]: [tex]\( 37,000 - 27,000 = 10,000 \)[/tex]
2. Calculate the time to recover the cost of college:
- For Person A:
- Total Cost of College: [tex]$45,000
- Increase in Salary: $[/tex]15,000
- Time to Recover Cost, [tex]\( T_A \)[/tex]: [tex]\( \frac{45,000}{15,000} = 3 \text{ years} \)[/tex]
- For Person B:
- Total Cost of College: [tex]$30,000
- Increase in Salary: $[/tex]10,000
- Time to Recover Cost, [tex]\( T_B \)[/tex]: [tex]\( \frac{30,000}{10,000} = 3 \text{ years} \)[/tex]
3. Compare the time to recover the investments:
- [tex]\( T_A \)[/tex] is 3 years
- [tex]\( T_B \)[/tex] is 3 years
Both Person A and Person B recover their investments in education in the same amount of time, which is 3 years.
### Conclusion:
Given this analysis, the correct answer is:
c. They recover their investments in the same amount of time.
