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

\begin{tabular}{|c|c|c|c|c|}
\hline & \begin{tabular}{c}
Salary prior to \\
school
\end{tabular} & \begin{tabular}{c}
Years attending \\
college
\end{tabular} & Total cost of college & \begin{tabular}{c}
Salary upon \\
graduating
\end{tabular} \\
\hline Person A & [tex]$\$[/tex] 18,000[tex]$ & 3 & $[/tex]\[tex]$ 45,000$[/tex] & [tex]$\$[/tex] 33,000[tex]$ \\
\hline Person B & $[/tex]\[tex]$ 27,000$[/tex] & 4 & [tex]$\$[/tex] 30,000[tex]$ & $[/tex]\[tex]$ 37,000$[/tex] \\
\hline
\end{tabular}

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.



Answer :

Let’s break down the problem step-by-step and solve it.

### Step 1: Calculate the total lost income during college for both persons
1. Person A:
- Salary prior to school: \[tex]$18,000 per year - Years attending college: 3 years - Total cost of college: \$[/tex]45,000

Total lost income = (Salary prior to school * Years attending college) + Total cost of college
[tex]\[ \text{Total lost income for Person A} = (18000 \times 3) + 45000 = 54000 + 45000 = 99000 \][/tex]

2. Person B:
- Salary prior to school: \[tex]$27,000 per year - Years attending college: 4 years - Total cost of college: \$[/tex]30,000

Total lost income = (Salary prior to school * Years attending college) + Total cost of college
[tex]\[ \text{Total lost income for Person B} = (27000 \times 4) + 30000 = 108000 + 30000 = 138000 \][/tex]

### Step 2: Calculate the yearly gain in salary after graduating
1. Person A:
- Salary upon graduating: \[tex]$33,000 - Salary prior to school: \$[/tex]18,000

Yearly gain in salary:
[tex]\[ \text{Yearly gain for Person A} = 33000 - 18000 = 15000 \][/tex]

2. Person B:
- Salary upon graduating: \[tex]$37,000 - Salary prior to school: \$[/tex]27,000

Yearly gain in salary:
[tex]\[ \text{Yearly gain for Person B} = 37000 - 27000 = 10000 \][/tex]

### Step 3: Calculate the number of years to recover the investments
1. Person A:
[tex]\[ \text{Years to recover investment for Person A} = \frac{\text{Total lost income}}{\text{Yearly gain}} = \frac{99000}{15000} = 6.6 \text{ years} \][/tex]

2. Person B:
[tex]\[ \text{Years to recover investment for Person B} = \frac{\text{Total lost income}}{\text{Yearly gain}} = \frac{138000}{10000} = 13.8 \text{ years} \][/tex]

### Conclusion
Person A recovers their investment in 6.6 years, whereas Person B takes 13.8 years.

Thus, the correct answer is:
a. Person A recovers their investment in a shorter amount of time.