To solve this problem, let's proceed step-by-step to determine which person recovers their investment in a shorter amount of time.
### Step 1: Calculate the salary increase after graduation
First, we need to determine the increase in salary each person experiences after they graduate from college.
1. Person A:
- Salary prior to college: [tex]$\$[/tex]18,000[tex]$
- Salary upon graduating: $[/tex]\[tex]$33,000$[/tex]
- Increase in salary = [tex]$\$[/tex]33,000 - \[tex]$18,000 = \$[/tex]15,000[tex]$
2. Person B:
- Salary prior to college: $[/tex]\[tex]$27,000$[/tex]
- Salary upon graduating: [tex]$\$[/tex]37,000[tex]$
- Increase in salary = $[/tex]\[tex]$37,000 - \$[/tex]27,000 = \[tex]$10,000$[/tex]
### Step 2: Calculate the recovery time for the investment
Next, we determine how long it takes each person to recover the total cost of their college education with their increased salary.
1. Person A:
- Total cost of college: [tex]$\$[/tex]45,000[tex]$
- Increase in salary: $[/tex]\[tex]$15,000$[/tex]
- Recovery time = Total cost of college / Increase in salary
- Recovery time for Person A = [tex]$\$[/tex]45,000 / \[tex]$15,000 = 3$[/tex] years
2. Person B:
- Total cost of college: [tex]$\$[/tex]30,000[tex]$
- Increase in salary: $[/tex]\[tex]$10,000$[/tex]
- Recovery time = Total cost of college / Increase in salary
- Recovery time for Person B = [tex]$\$[/tex]30,000 / \[tex]$10,000 = 3$[/tex] years
### Step 3: Compare the recovery times
Both Person A and Person B have a recovery time of 3 years. Therefore, they both recover their investments in the same amount of time.
### Conclusion
The correct statement is:
c. They recover their investments in the same amount of time.
