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Question 1125804: Deandre bought a desktop computer and a laptop computer. Before finance charges, the laptop cost
$300 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 7% per year. The total finance charges for one year were $365. How much did each computer cost before finance charges?
Answer by kasperk(4)   (Show Source):
You can put this solution on YOUR website! Let $D = cost of the desktop
Then $D + $300 = cost of the laptop
DESKtop computer:
Principal amount = D
r = 9% = .09
t = 1 year
Therefore, using a simple interest formula I = Prt, we find I = D·(0.09)·1 = 0.09D
LAPtop computer:
Principal amount = D+300
r = 7% = .07
t = 1 year
Therefore, I = Prt = (D+300)·(0.07)·1 = 0.07(D+300) = 0.07D + 21
If we add up the interest on the desktop and the interest on the laptop, that total interest should equal $365 (interestingly, $1 per day of the year!):
0.09D + 0.07D + 21 = 365
Combine like terms:
0.16D + 21 = 365
Subtract 21 from each side of the equation:
0.16D = 344
Divide both sides of the equation by 0.16:
D = $2150 = desktop computer cost
D + 300 = $2450 = laptop computer cost
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