frank borrowed money from his dad to buy a motorcycle. to repay his loan, frank paid his dad $200 each…

frank borrowed money from his dad to buy a motorcycle. to repay his loan, frank paid his dad $200 each month. after 14 months, his remaining debt was $3,200. • r represents the remaining debt at a given time. • l represents the original loan amount. • t represents the time (in months). which three statements are correct? a the original loan amount was $6,000. b it will take frank 16 months to pay back his dad. c it will take frank 30 months to pay back his dad. d the equation r = l - 200t can be used to model this situation. e the equation l = r - 200t can be used to model this situation.

frank borrowed money from his dad to buy a motorcycle. to repay his loan, frank paid his dad $200 each month. after 14 months, his remaining debt was $3,200. • r represents the remaining debt at a given time. • l represents the original loan amount. • t represents the time (in months). which three statements are correct? a the original loan amount was $6,000. b it will take frank 16 months to pay back his dad. c it will take frank 30 months to pay back his dad. d the equation r = l - 200t can be used to model this situation. e the equation l = r - 200t can be used to model this situation.

Answer

Explanation:

Step1: Analyze the loan - repayment formula

The general formula for loan - repayment is $R = L-200T$, where $L$ is the original loan amount, $T$ is the time in months, and $R$ is the remaining debt. We know that $L = 3200$ (original loan amount) and the monthly payment is $200$.

Step2: Find the time to pay off the loan

To find the time $T$ it takes to pay off the loan, we set $R = 0$ (when the debt is fully repaid). So, $0 = L-200T$, which gives $T=\frac{L}{200}$. Substituting $L = 3200$ into the formula, we get $T=\frac{3200}{200}=16$ months.

Step3: Check the statements

  • Statement A: The original loan amount was $3200$, not $6000$, so statement A is incorrect.
  • Statement B: Since $T = 16$ months when $R = 0$, it will take Frank 16 months to pay back his dad, so statement B is correct.
  • Statement C: It takes 16 months, not 30 months, so statement C is incorrect.
  • Statement D: The correct formula is $R = L - 200T$, not $R = L-200T$ written as $L=R - 200T$, so statement D is incorrect.
  • Statement E: The correct formula is $R = L - 200T$, not $L = R-200T$, so statement E is incorrect.

Answer:

B. It will take Frank 16 months to pay back his dad.