Hi I need help solving this word problem thanks for the help

Question

Kira bought a desktop computer and a laptop computer. Before charges, the laptop costs $300 more than the desktop. she paid for the computera 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 of finance charges of one year were $398. How much did each computer cost before finance charges.

 

Thank you for helping in advance I am just completely stuck on this one 

 

Answer 1

Let x = price of the desktop computer

     (x+300) = price of the laptop computer    ["$300 more than the desktop"]

 

"The total of finance charges of one year were $398"     means

    one-year finance charge for desktop  +  one-year finance charge for laptop  =  $398

                 (6/100)x                            +                   (7/100)(x+300)            =   398

 

Note:  6% may be written as 0.06 or (6/100) as needed by the problem.

 

The key point is that the problem gives the total interest charges for one year, the two interest rates, and the difference in the initial costs.  So, we may calculate the initial costs.

 

The math:

    (6/100)x + (7/100)(x+300) = 398

     6x + 7(x+300) = 39800              [multiply both sides by 100 to get rid of fractions]

     6x + 7x + 2100 = 39800            [distribute]

       13x = 37700                          [subtract 2100 from both sides]

          x = 2900                   [divide both sides by 13]

 

The desktop computer cost $2900.

The laptop computer cost $3200.

 

Check:

  (6/100)2900 + (7/100)3200 = 398   ?

       174         +     224          = 398   ?

                   398                  =  398   ?yes