Question

Ahmad bought a desktop computer and a laptop computer. Before finance charges, the laptop cost less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was per year, and for the laptop it was per year. The total finance charges for one year were . How much did each computer cost before finance charges?

Answer 1

The question seems to be missing some key figures. Below is what I believe you intended.

Ahmad bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $450 less than the desktop. 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. The total finance charges for one year were $276. How much did each computer cost before finance charges?

Answer:

The desktop computer costs $2,406 before finance charges while the laptop costs $1956 before finance charges too.

Step-by-step explanation:

X = price of a desktop computer

Y = price of a laptop computer

the price of the laptop computer is $450 less than the price of

a desktop computer.

this means that y = x - $450.

i1 = interest on desktop computer.

i2 = interest on laptop computer.

i1 = .07 * x

i2 = .055 * Y

the total finance charges for one year are $276.

this means that i1 + i2 = $276 which means that .07x + .055y =

$276.

since y = x - $450, this formula becomes .07x + .055(x-$450) =

$276.

simplify to get .07x + .055x - 24.75 = $276.

combine like terms to get .125x - 24.75 = $276.

add 24.75 to both sides of the equation to get .125x = $300.75

divide both sides of this equation by .125 to get x = $2,406

since y = x - 450, this means that y is equal to $1,956

the desktop computer cost $2,406

the laptop computer cost $1,956

.07 * $2,406 = $168.42

.055* $1,956 = $107.58

$168.42 + $107.58 = $276.00.

solution is confirmed to be correct.

the desktop computer cost $2,406 before the finance charge

was applied.

the laptop computer cost $1,956 before the finance charge was

applied.

Answer 2

cost of laptop = $1,800

cost of desktop = $2,100

Step-by-step explanation:

From the question above, we can see that the laptop costs $300 less than the desktop, therefore, we say:

let x represent the cost of the laptop ;

then x+300 will be the cost of the desktop .

We can also see that the total finance charge of $252 is equal to 7% of the cost of the laptop and 6% of the cost of the desktop, we solve as follows:

252 = 0.07(x) + 0.06(x + 300)

252 = 0.07x + 0.06x + 18

252 - 18 = 0.13x

234 = 0.13x

x = 234/0.13

x = 1,800

Recall that:

cost of desktop = x + 300

therefore:

1,800 + 300 = 2,100.

cost of laptop = $1,800

cost of desktop = $2,100