Let's break down the problem to determine how long it takes each person to recover their investment in education.
### Person A:
1. Salary prior to school: \[tex]$18,000
2. Years attending college: 3
3. Total cost of college: \$[/tex]45,000
4. Salary upon graduating: \[tex]$33,000
Step-by-Step Calculation for Person A:
1. Loss of income during college:
\[
18,000 \, \text{USD/year} \times 3 \, \text{years} = 54,000 \, \text{USD}
\]
2. Total investment (cost of college + loss of income):
\[
54,000 \, \text{USD (loss of income)} + 45,000 \, \text{USD (cost of college)} = 99,000 \, \text{USD}
\]
3. Extra annual income after graduating:
\[
33,000 \, \text{USD} - 18,000 \, \text{USD} = 15,000 \, \text{USD}
\]
4. Years to recover the investment:
\[
\frac{99,000 \, \text{USD}}{15,000 \, \text{USD/year}} = 6.6 \, \text{years}
\]
### Person B:
1. Salary prior to school: \$[/tex]27,000
2. Years attending college: 4
3. Total cost of college: \[tex]$30,000
4. Salary upon graduating: \$[/tex]37,000
Step-by-Step Calculation for Person B:
1. Loss of income during college:
[tex]\[
27,000 \, \text{USD/year} \times 4 \, \text{years} = 108,000 \, \text{USD}
\][/tex]
2. Total investment (cost of college + loss of income):
[tex]\[
108,000 \, \text{USD (loss of income)} + 30,000 \, \text{USD (cost of college)} = 138,000 \, \text{USD}
\][/tex]
3. Extra annual income after graduating:
[tex]\[
37,000 \, \text{USD} - 27,000 \, \text{USD} = 10,000 \, \text{USD}
\][/tex]
4. Years to recover the investment:
[tex]\[
\frac{138,000 \, \text{USD}}{10,000 \, \text{USD/year}} = 13.8 \, \text{years}
\][/tex]
### Conclusion:
Comparing the recovery times:
- Person A needs 6.6 years to recover their investment.
- Person B needs 13.8 years to recover their investment.
Therefore, Person A recovers their investment in a shorter amount of time. Thus, the correct answer is:
a. Person A recovers their investment in a shorter amount of time.
