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

Question

Maria bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $300 less 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 6% per year. The total finance charges for one year were $398. 

How much did each computer cost before finance charges?

Desktop:

Laptop:

Answer 1

Hope this helps...

Need to solve TWO linear equations simultaneously...

L = Cost of the Laptop

D = Cost of the desktop

We know the Laptop is $300 less than the Desktop...so L = D - 300 OR D - L = 300

The 2nd equation is the finance charges...

D(0.07) + L(0.06) = 398

So...

1st equation: D - L = 300

2nd equation: D(0.07) + L(0.06) = 398

Apply a factor so that we can eliminate ONE of the terms so when we add the equation, that term drops out

Multiply the 1st equation (both sides) by -0.07...... (-0.07)(D - L) = 300(-0.07) = -0.07D + 0.07L = -21

Add the modified 1st equation to the 2nd equation;;

-0.07D + 0.07L = -21

0.07D + 0.06L = 398 ....D term cancels out (REMEMBER, you are adding the equations)

0.13L = 377

L = $ 2900 ... That is the original cost of the laptop, then

D = $ 3200 (because its $300 more

You can CHECK by calculating the finance charges on each;

L (finance charge) = $2900(0.06) = $174

D (finance charge) = $3200(0.07) = $224

The total finance charge is $174 + $224 = $398