Question

Lucy bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $150 more than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $303. How much did each computer cost before finance charges?

Answer 1

Let x be the cost before finance charges of the desktop computer.

The laptop cost $150 more than the desktop; the cost of the laptop is: x+150

For the desktop the interest rate was 7% per year: multiply the cost before finance charges by the interest rate in decimal form to get the finance charges for one year: 0.07x

For the laptop it was 9.5% per year: 0.095(x+150)

As the total finance charges for one year were $303 you get the next equation:

$0.07x+0.095(x+150)=303$

Use the equation to solve x:

$\begin{gathered} 0.07x+0.095x+14.25=303 \\ 0.165x=303-14.25 \\ 0.165x=288.75 \\ x=\frac{288.75}{0.165} \\ \\ x=1750 \end{gathered}$

Use x to find the cost of each computer cost before finance charges:

Desktop computer:

$x=1750$

Laptop:

$x+150=1750+150=1900$Then, the cost before finance charges is: for the desktop $1750 and for the Laptop $1900