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?
