Solving a tax rate or interest rate problem using a system of linear equations

Question

Jina bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $300 more than the desktop. She 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 $365. 

How much did each computer cost before finance charges?

Desktop:

Laptop:

Answer 1

Well suppose the laptop cost l, the desktop d.

Then l = d + 300

Financing charges were 9% of d = 0.09d for the desktop

and 7% of l for the laptop = 0.07l

So 0.09d + 0.07l = 365

9d + 7l = 36500

l = d + 300

9d + 7 (d+300) = 36500

16d + 2100 = 36500

16d = 34400

d = 2150

l = 2450

2150 x 0.09 + 2450 x 0.07 = 365 (checking our answer)