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.\nplease select the best answer from the choices provided

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.\nplease select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate Person A's lost - income

Person A's salary prior to school is $18000$ and attended college for $3$ years. Lost - income = $18000\times3=$54000$. Total investment = lost - income+total cost of college = $54000 + 45000=$99000$. The increase in salary after graduating is $33000 - 18000=$15000$ per year. Time to recover investment = $\frac{99000}{15000}=6.6$ years.

Step2: Calculate Person B's lost - income

Person B's salary prior to school is $27000$ and attended college for $4$ years. Lost - income = $27000\times4=$108000$. Total investment = lost - income+total cost of college = $108000+30000=$138000$. The increase in salary after graduating is $37000 - 27000=$10000$ per year. Time to recover investment = $\frac{138000}{10000}=13.8$ years.

Step3: Compare the recovery times

Since $6.6<13.8$, Person A recovers their investment in a shorter amount of time.

Answer:

a. Person A recovers their investment in a shorter amount of time.