Question

Raul has $460 in his checking account. Each month, $45 is automatically deducted from his account to pay for his cell phone plan. He makes no other deposits or withdrawals. He wants to always have more than $100 in his account. What is the greatest number of months he can pay for his cell phone and still have more than $100 in his account?
7 months
8 months
9 months
10 months

Answer 1

Let n be the number of months. After n months the balance is 460 − 45n, and we need 460 − 45n > 100.
So 45n < 360 ⇒ n < 8. The greatest whole number n is 7.

Check: 460 − 45·7 = 145 (>100), but 460 − 45·8 = 100 (not >100).
Answer: 7 months.