two people quit work and begin college at the same time. their salary and education information is given in…

two people quit work and begin college at the same time. their salary and education information is given in the table below.\n| | salary prior to school | years attending college | total cost of college | salary upon graduating |\n|--|--|--|--|--|\n| person a | $18,000 | 3 | $45000 | $33,000 |\n| person b | $27,000 | 4 | $30,000 | $37,000 |\nchoose the true statement.\na. person a recovers their investment in a shorter amount of time.\nb. person b recovers their investment in a shorter amount of time.\nc. they recover their investments in the same amount of time.\nd. there is too little information to compare the time to recover their investments.
Answer
Explanation:
Step1: Calculate Person A's total investment
Total investment = Lost - salary + College - cost. Lost - salary for Person A is $18000\times3$, and college - cost is $45000$. So total investment $I_A=18000\times3 + 45000=54000 + 45000=99000$.
Step2: Calculate Person A's annual salary - gain
Annual salary - gain for Person A is $33000 - 18000 = 15000$.
Step3: Calculate time for Person A to recover investment
Time $t_A=\frac{I_A}{Annual - salary - gain}=\frac{99000}{15000}=6.6$ years.
Step4: Calculate Person B's total investment
Lost - salary for Person B is $27000\times4$, and college - cost is $30000$. So total investment $I_B=27000\times4+30000 = 108000+30000=138000$.
Step5: Calculate Person B's annual salary - gain
Annual salary - gain for Person B is $37000 - 27000 = 10000$.
Step6: Calculate time for Person B to recover investment
Time $t_B=\frac{I_B}{Annual - salary - gain}=\frac{138000}{10000}=13.8$ years.
Answer:
a. Person A recovers their investment in a shorter amount of time.