MHB How Much Did Each Computer Cost Before Finance Charges?

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Jim purchased a desktop computer for $1,750 and a laptop for $1,900 before finance charges. The laptop's price was $150 more than the desktop's. He financed the desktop at a 7% interest rate and the laptop at 5.5%. The total finance charges for one year amounted to $227. The calculations confirmed the costs of both computers based on the given equations.
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Jim bought a desktop computer and a laptop computer. Before finance charges, the laptop cost \$150 more than the desktop. He 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 5.5% per year. The total finance charges for one year were \$227.

How much did each computer cost before finance charges?
 
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Hello, and welcome to MHB! (Wave)

I re-titled your thread so that the title reflects the question being asked. So, let's walk through this problem.

jesspowers526 said:
Jim bought a desktop computer and a laptop computer.

Let's let \(D\) be the cost of the desktop computer and \(L\) be the cost of the laptop computer. These costs will be in dollars.

jesspowers526 said:
Before finance charges, the laptop cost \$150 more than the desktop.

From this, we may write:

$$L=D+150$$

jesspowers526 said:
He 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 5.5% per year.

So, the finance charge for the desktop is \(0.07D\) and the finance charge for the laptop is \(0.055L\).

jesspowers526 said:
The total finance charges for one year were \$227.

This allows us to write:

$$0.07D+0.055L=227$$

I would first multiply this equation by 1000 to get rid of the decimals:

$$70D+55L=227000$$

Now divide by 5:

$$14D+11L=45400$$

jesspowers526 said:
How much did each computer cost before finance charges?

We have two unknowns, which are what we're being asked to find, and two equations, so we may determine a unique solution. I would use the first equation to substitute for \(L\) into the second equation, giving us an equation in \(D\) alone, which we can then solve:

$$14D+11(D+150)=45400$$

Distribute:

$$14D+11D+1650=45400$$

Combine like terms:

$$25D=43750$$

Divide by 25:

$$D=1750$$

Now, we may use the first equation to find \(L\):

$$L=D+150=1750+150=1900$$

Thus, we have determined the cost of the desktop computer is \$1750 and the cost of the laptop computer is \$1900. Does all of that make sense?
 
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