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Reuben 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?

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Answer:

The cost of desktop is [tex]\$2100[/tex] and the laptop is [tex]\$1800[/tex]

Solution:

Let us assume the desktop cost [tex]\$ x[/tex] and laptop costs [tex]\$ y[/tex]

Now, the laptop cost $300 less than the desktop,

So, [tex]x = y+300[/tex] ………… (i)

Again the desktop the interest rate was [tex]6\%[/tex] per year = 0.06x

For the laptop it was [tex]7\%[/tex] per year = 0.07y

The total finance charges for one year were [tex]\$ 252[/tex]

So, [tex]0.06x + 0.07y = 252[/tex]  

[tex]0.06 (y +300) +0.07- 252 = 0[/tex] (value from (i))

[tex]0.06y + 18 +0.07-252 = 0[/tex]

[tex]0.13y =234[/tex]

[tex]y = 1800[/tex]

Hence [tex]x = (1800+300) = 2100[/tex]

The desktop costs [tex]\$2100[/tex] and the laptop costs [tex]\$1800[/tex]

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