Question

Jim bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $300 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 6% per year, and for the laptop it was 7% per year. The total finance charges for one year were $252. How much did each computer cost before finance charges?

Answer 1

L := laptop

D := desktop

before finance, equation 1:

`L=D-300`

Di = 6% = 0.06 (desktop interest per year)

Li = 7% = 0.07 (laptop interest per year)

For one year, the total finance charge is (equation 2):

`(L\cdot Li)+(D\cdot Di)=252`

We substitute L (the equation 1) to the equation 2:

`\begin{gathered} \lbrack(D-300)\cdot Li\rbrack+(D\cdot Di)=252 \\ (D\cdot Li)-(300\cdot Li)+(D\cdot Di)=252 \\ 0.07\cdot D+0.06\cdot D=252+(300)\cdot(0.07) \\ 0.13D=273 \\ D=(273)/(0.13) \\ D=2100 \end{gathered}`

Then we substitute the value D in equation 1 to find the laptop price:

`L=D-300=2100-300=1800`

Therefore, the laptop and desktop prices are $1800 and $2100, respectively.