Question

Jessica bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $450 less than the desktop. She paid for the computers using two different financing plans. For the desktop the internet rate was 6.5% per year, and the for laptop it was 9% per year. The total finance charges for one year were $409. How much did each computer cost before finance charges?

Answer 1

Step 1 :

In this question, we have that Jessica bought a desktop computer and a laptop computer.

Before finance charges, the laptop cost $450 less than the desktop.

This means that:

`\begin{gathered} \text{Let L = cost of the laptop = D - 450} \\ D=\text{ cost of the desktop } \end{gathered}`

Step 2 :

The total finance charge for one year is given by :

`\begin{gathered} (\text{ 6.5 \% of D ) + ( 9 \% of L ) = 409} \\ (\text{ 0. 065 x D ) + ( 0.09 X ( D - 450 ) ) = 409} \\ 0.065\text{ D + 0.09 D - 40. 5 = 409} \end{gathered}`
`\begin{gathered} \text{Simplifying further, we have that:} \\ 0.065\text{ D + 0.09 D = 409 + 40. 5} \\ 0.155\text{ D = 449.5} \end{gathered}`
`\begin{gathered} \text{Dividing both sides by 0.155, we have that:} \\ D\text{ =}\frac{449.\text{ 5}}{0.155} \\ D\text{ = }2900 \end{gathered}`

Step 3:

Recall that the cost of the Laptop = D - 450

This means that :

`2900\text{ - 450 = 2450}`

Check:

`\begin{gathered} (\text{ 6. 5\% of 2900 ) + ( 9 \% of 2450 ) } \\ =\text{ 188. 50 + 220. 50 = \$ 409} \end{gathered}`

CONCLUSION:

The cost of the Desktop before the finance charges = $ 2900

The cost of the Laptop before the fiance charges = $ 2450.