Question 1134608: Kevin 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)   (Show Source):
You can put this solution on YOUR website! let D equal the price of the desktop.
let L equal the price of the laptop.
the laptop costs 200 less than the desktop.
that gets you L = D - 200
the finance charge for the desktop was 9% and the finance charge for the laptop was 7% and the total finance charges were $306 for one year.
that gets you .09 * D + .07 * L = 306.
in the second equation, replace L with D - 200 to get.09 * D + .07 * (D - 200) = 306.
simplify to get .09 * D + .07 * D - .07 * 200 = 306.
simplify further and combine like terms to get .16 * D - 14 = 306.
add 14 to both sides of the equation to get .16 * D = 320.
solve for D to get D = 2000.
since L = D - 200, then L = 1800.
the cost of the desktop is 2000 and the cost of the laptop is 1800.
the total finance charge for one year is equal to .09 * the desktop and .07 * the laptop.
that makes the total finance charge for the year equal to .09 * 2000 + .07 * 1800 = 306.
solution looks good.
solution is that the desktop cost $2000 and the laptop cost $1800 before the finance charges were applied.
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