SOLUTION: Trey bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $200 less than the desktop. He paid for the computers using two different financing

Algebra ->  Finance -> SOLUTION: Trey bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $200 less than the desktop. He paid for the computers using two different financing      Log On


   

Question 1031124: Trey bought a desktop computer and a laptop computer. Before finance charges, the laptop cost
$200
less 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
$306
. How much did each computer cost before finance charges?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = price of a desktop computer
y = price of a laptop computer

the price of the laptop computer is 200 less than the price of a desktop computer.

this means that y = x - 200.

i1 = interest on desktop computer.
i2 = interest on laptop computer.

i1 = .09 * x
i2 = .07 * y

the total finance charges for one year are 306.

this means that i1 + i2 = 306 which means that .09x + .07y = 306.

since y = x - 100, this formula becomes .09x + .07(x-200) = 306.

simplify to get .09x + .07x - 14 = 306

combine like terms to get .16x - 14 = 306.

add 14 to both sides of the equation to get .16x = 320.

divide both sides of this equation by .16 to get x = 2000.

since y = x - 100, this means that y is equal to 1800.

the desktop computer cost 2000.
the laptop computer cost 1800.

.09 * 2000 = 180.
.07 * 1800 = 126.

180 + 126 = 306.

solution is confirmed to be correct.

the desktop computer cost 2000 before the finance charge was applied.
the laptop computer cost 1800 before the finance charge was applied.