MHB How Much Did Each Computer Cost Before Finance Charges?

[jesspowers526]

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?

 

[MarkFL]

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.

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.

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

From this, we may write:

$$L=D+150$$

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 \(0.055L\).

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:

$$14D+11L=45400$$

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?