Question

Solving a tax rate or interest rate problem using a system of equations - Lisa bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $400 less than the desktop. She paid for the computers with 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?

A) Desktop cost: $1,600; Laptop cost: $1,200
B) Desktop cost: $1,200; Laptop cost: $800
C) Desktop cost: $1,800; Laptop cost: $1,400
D) Desktop cost: $2,000; Laptop cost: $1,600

Answer 1

The answer of the given statement that "each computer cost before finance charges" is C) Desktop cost: $1,800; Laptop cost: $1,400

Step-by-step explanation:

Let's denote the cost of the desktop computer as \(D\) and the cost of the laptop computer as \(L\).

According to the given information, the laptop cost $400 less than the desktop, so we can write the equation:

\[ L = D - 400 \]

The total finance charges for one year, considering the interest rates for each computer, is $371. The finance charge for the desktop (\(0.075D\)) plus the finance charge for the laptop (\(0.08L\)) equals the total finance charges:

\[ 0.075D + 0.08L = 371 \]

Now, substitute the expression for \(L\) from the first equation into the second equation:

\[ 0.075D + 0.08(D - 400) = 371 \]

Solve this system of equations to find \(D\) and \(L\). The solution is \(D = 1,800\) and \(L = 1,400\).

Therefore, the correct answer is C) Desktop cost: $1,800; Laptop cost: $1,400.