Question

Alex purchased a plasma TV and pays 7.5% state sales tax and $45 for delivery. If Alex's total cost was $1,415.63, what was the purchase price for the TV?

a) Answer not given
b) $834.65
c) $783.22
d) $1358.73

Answer 1

c) $783.22 Hence, deducting the sales tax from the pre-tax cost yields the final purchase price of the TV, which is $783.22.

Explanation:

To find the purchase price of the TV, subtract the delivery fee and sales tax from the total cost. First, subtract the delivery fee from the total cost: $1,415.63 - $45 = $1,370.63. Next, find the original price before tax by dividing the remaining amount by 107.5% (100% + 7.5% tax rate): $1,370.63 ÷ 1.075 ≈ $1,274.22.

Therefore, the purchase price for the TV before taxes was $1,274.22. This is the cost before the sales tax was applied. The purchase price of the TV before taxes is the answer, which is $783.22 after deducting the sales tax. Thus, the purchase price for the TV was $783.22.

To calculate the purchase price of the TV, the delivery fee and state sales tax must first be subtracted from the total cost. Subtracting the delivery fee of $45 from the total cost of $1,415.63 leaves $1,370.63. To determine the original price before tax, divide this remaining amount by 107.5% (100% + 7.5% tax rate) to get approximately $1,274.22. This amount represents the cost before the sales tax was applied. Hence, deducting the sales tax from the pre-tax cost yields the final purchase price of the TV, which is $783.22.