Let's carefully analyze the given information step-by-step:
1. Calculate the Lost Income During College:
- Person A: Salary prior to school is \[tex]$18,000 per year and they attend college for 3 years.
\[
\text{Lost Income for Person A} = 18000 \times 3 = \$[/tex]54000
\]
- Person B: Salary prior to school is \[tex]$27,000 per year and they attend college for 4 years.
\[
\text{Lost Income for Person B} = 27000 \times 4 = \$[/tex]108000
\]
2. Calculate the Total Investment in College:
- Person A: Total cost of college is \[tex]$45,000.
\[
\text{Total Investment for Person A} = \text{Lost Income} + \text{Cost of College} = 54000 + 45000 = \$[/tex]99000
\]
- Person B: Total cost of college is \[tex]$30,000.
\[
\text{Total Investment for Person B} = \text{Lost Income} + \text{Cost of College} = 108000 + 30000 = \$[/tex]138000
\]
3. Calculate the Salary Increase After Graduating:
- Person A: Salary upon graduating is \[tex]$33,000.
\[
\text{Salary Increase for Person A} = 33000 - 18000 = \$[/tex]15000
\]
- Person B: Salary upon graduating is \[tex]$37,000.
\[
\text{Salary Increase for Person B} = 37000 - 27000 = \$[/tex]10000
\]
4. Calculate the Time to Recover the Investment:
- Person A:
[tex]\[
\text{Time to Recover Investment for Person A} = \frac{\text{Total Investment}}{\text{Salary Increase}} = \frac{99000}{15000} = 6.6 \text{ years}
\][/tex]
- Person B:
[tex]\[
\text{Time to Recover Investment for Person B} = \frac{\text{Total Investment}}{\text{Salary Increase}} = \frac{138000}{10000} = 13.8 \text{ years}
\][/tex]
5. Compare the Recovery Times:
- Person A takes 6.6 years to recover their investment.
- Person B takes 13.8 years to recover their investment.
Therefore, Person A recovers their investment in a shorter amount of time.
Hence, the correct choice is:
a. Person A recovers their investment in a shorter amount of time.
