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]$18,000 & 3 & \$[/tex]45,000 & \[tex]$33,000 \\
\hline Person B & \$[/tex]27,000 & 4 & \[tex]$30,000 & \$[/tex]37,000 \\
\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.



Answer :

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.