Answer:
B. 10 months
Step-by-step explanation:
The balance on the loan will be ...
b = 1600 - 80t . . . . . . where t is the number of months of payments
The balance in the savings account will be ...
s = 500 + 25t
The savings account balance will be at least as much as the loan balance when ...
s ≥ b
500 +25t ≥ 1600 -80t . . . substitute the account balance expressions
105t ≥ 1100 . . . . . . . . . . . . add 80t -500
t ≥ 1100/105 ≈ 10.48 ≈ 10
It will take Josh 10 months to have enough savings to pay the loan in full.
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<em>Comment on rounding</em>
IMO, it makes no sense to round down, as Josh will NOT have enough in 10 months. He will have enough after he makes one more payment of $80. At 10 months, the loan balance is $50 more than the savings balance. It will be 11 months before there is enough savings to pay off the loan.
