scott bought a desktop computer and a laptop computer. before finance charges, the laptop cost $400 less…

scott bought a desktop computer and a laptop computer. before finance charges, the laptop cost $400 less than the desktop. he paid for the computers using two different financing plans. for the desktop the interest rate was 7.5% per year, and for the laptop it was 8% per year. the total finance charges for one year were $371. how much did each computer cost before finance charges? note that the aleks graphing calculator can be used to make computations easier. desktop: $ laptop: $
Answer
Explanation:
Step1: Let the cost of the desktop be $x$.
Then the cost of the laptop is $x - 400$.
Step2: Calculate the finance - charge for the desktop.
The finance - charge for the desktop at a rate of 7.5% per year is $0.075x$.
Step3: Calculate the finance - charge for the laptop.
The finance - charge for the laptop at a rate of 8% per year is $0.08(x - 400)$.
Step4: Set up the equation for the total finance - charges.
The total finance charges for one year is $371$, so $0.075x+0.08(x - 400)=371$.
Step5: Expand and simplify the equation.
$0.075x+0.08x-32 = 371$. Combining like terms gives $0.155x-32 = 371$.
Step6: Solve for $x$ (cost of the desktop).
Add 32 to both sides of the equation: $0.155x=371 + 32=403$. Then $x=\frac{403}{0.155}=2600$.
Step7: Calculate the cost of the laptop.
The cost of the laptop is $x - 400=2600 - 400 = 2200$.
Answer:
Desktop: $2600 Laptop: $2200