Dante bought a desktop computer and a laptop computer. Before finance charges, the laptop cost \( \$ 450 \) more than the fifferent financing plans. For the desktop the interest rate was \( 9 \% \) per year, and for the laptop it was \( 6 \% \) per year. The total finance charges for one year were \( \$ 300 \). How much did each computer cost before finance charges? Note that the ALEKS graphing calculator can be used to make computations easier.
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Let’s denote the cost of the desktop computer as \( D \) and the cost of the laptop computer as \( L \). According to the problem, we know: 1. \( L = D + 450 \) 2. The finance charges can be expressed as \( 0.09D + 0.06L = 300 \) To solve this, we can substitute the expression for \( L \) from the first equation into the second equation. Thus: \[ 0.09D + 0.06(D + 450) = 300 \] This simplifies to: \[ 0.09D + 0.06D + 27 = 300 \] \[ 0.15D + 27 = 300 \] Subtracting 27 from both sides: \[ 0.15D = 273 \] Now, divide by 0.15: \[ D = \frac{273}{0.15} = 1820 \] Now that we have the cost of the desktop, we can find the cost of the laptop: \[ L = D + 450 = 1820 + 450 = 2270 \] So, the final answer is that the desktop computer costs \( \$1820 \) and the laptop computer costs \( \$2270 \).
