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.
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.
