Question

Rudolph borrowed $650 from his parents to make some repairs on his car. He promised to repay the loan by giving his parents at least $76 from his paycheck each week. Assuming Rudolph sticks to his promise, which of the following is not a possible scenario for the amount of debt Rudolph has remaining?

After 5 weeks, Rudolph is $285 in debt.

After 6 weeks, Rudolph is $185 in debt.

After 7 weeks, Rudolph is $100 in debt.

After 8 weeks, Rudolph is $40 in debt

Answer 1

Rudolph borrowed $650 from his parents to make some repairs on his car. He promised to repay the loan by giving his parents at least $76 from his paycheck each week. Assuming Rudolph sticks to his promise, which of the following is not a possible scenario for the amount of debt Rudolph has remaining?

Which is not possible.
After 5 weeks, Rudolph is $285 in debt.
After 6 weeks, Rudolph is $185 in debt.
After 7 weeks, Rudolph is $100 in debt.
After 8 weeks, Rudolph is $40 in debt

Identify the claims being made that are relevant to answering the question.

$650 is owed.
At least $76 is paid each week.

Week 1 Maximum = $650 - $76 = $574 Debt
Week 2 Maximum = $650 - $152 = $498 Debt
Week 3 Maximum = $650 - $228 = $422 Debt
Week 4 Maximum = $650 - $304 = $346 Debt
Week 5 Maximum = $650 - $380 = $270 Debt
Week 6 Maximum = $650 - $456 = $194 Debt
Week 7 Maximum = $650 - $532 = $118 Debt
Week 8 Maximum = $650 - $608 = $42 Debt

The minimum possible debt is $0 if the full amount is paid at any time.

After 5 weeks, Rudolph is $285 in debt - After Week 5 Range is $0 - $270. Not Possible
After 6 weeks, Rudolph is $185 in debt - After Week 6 Range is $0 - $194. Possible.
After 7 weeks, Rudolph is $100 in debt.- After Week 7 Range is $0 - $118. Possible.
After 8 weeks, Rudolph is $40 in debt. - After Week 8 Range is $0 - $42. Possible