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ail bought a desktop computer and a laptop computer. Before finance charges, the laptop cost US$250 less than the desktop. She paid for the computers using two different 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 US$300. How much did each computer cost before finance charges?

Question

ail bought a desktop computer and a laptop computer. Before finance charges, the laptop cost US250lessthanthedesktop.Shepaidforthecomputersusingtwodifferentfinancingplans.Forthedesktoptheinterestratewas9250 less than the desktop. She paid for the computers using two different 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 US300. How much did each computer cost before finance charges?

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Solution 1

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

According to the problem, the laptop cost $250 less than the desktop: L=D250 L = D - 250

The interest rate for the desktop is 9% per year, and for the laptop, it is 6% per year. The total finance charges for one year were $300. Therefore, we can write the equation for the total finance charges as: 0.09D+0.06L=300 0.09D + 0.06L = 300

Now, substitute the expression for L L from the first equation into the second equation: 0.09D+0.06(D250)=300 0.09D + 0.06(D - 250) = 300

Distribute the 0.06: 0.09D+0.06D15=300 0.09D + 0.06D - 15 = 300

Combine like terms: 0.15D15=300 0.15D - 15 = 300

Add 15 to both sides of the equation: 0.15D=315 0.15D = 315

Divide both sides by 0.15: D=2100 D = 2100

Now, substitute D=2100 D = 2100 back into the equation L=D250 L = D - 250 : L=2100250 L = 2100 - 250 L=1850 L = 1850

Therefore, the cost of the desktop computer before finance charges is 2100,andthecostofthelaptopcomputerbeforefinancechargesis2100, and the cost of the laptop computer before finance charges is 1850.

This problem has been solved

Solution 2

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

According to the problem, the laptop cost $250 less than the desktop: L=D250 L = D - 250

The interest rate for the desktop is 9% per year, and for the laptop, it is 6% per year. The total finance charges for one year were $300. Therefore, we can write the following equation for the total finance charges: 0.09D+0.06L=300 0.09D + 0.06L = 300

Now, substitute L L from the first equation into the second equation: 0.09D+0.06(D250)=300 0.09D + 0.06(D - 250) = 300

Simplify the equation: 0.09D+0.06D15=300 0.09D + 0.06D - 15 = 300 0.15D15=300 0.15D - 15 = 300

Add 15 to both sides of the equation: 0.15D=315 0.15D = 315

Divide both sides by 0.15: D=3150.15 D = \frac{315}{0.15} D=2100 D = 2100

Now, substitute D D back into the first equation to find L L : L=2100250 L = 2100 - 250 L=1850 L = 1850

Therefore, the cost of the desktop computer before finance charges was 2100,andthecostofthelaptopcomputerbeforefinancechargeswas2100, and the cost of the laptop computer before finance charges was 1850.

This problem has been solved

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