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Difficulty: HardPercentage Change, Markups, and Discounts

An industrial supply company purchases a heavy-duty welding machine directly from the manufacturer for $2,400.00\$2,400.00. The company applies a 40%40\% markup to establish their standard retail price. During a promotional event, a customer purchases the machine at a 15%15\% discount off the retail price. If an additional 6%6\% sales tax is applied to the discounted price, what is the total amount the customer pays in dollars?

Answer: 3027.36 $

Answer

3027.36
To find the final amount, each percentage change must be applied sequentially to the most recent price. First, the 40%40\% markup increases the $2,400.00\$2,400.00 base price to $3,360.00\$3,360.00. Next, the 15%15\% discount reduces this retail price to $2,856.00\$2,856.00. Finally, applying the 6%6\% sales tax to the discounted price yields a final total of $3,027.36\$3,027.36.

Step-by-Step Solution

1
Calculate the markup amount and the standard retail price.
$2,400.00×1.40=$3,360.00\$2,400.00 \times 1.40 = \$3,360.00
The 40%40\% markup is based on the initial wholesale cost.
2
Calculate the sale price after the discount.
$3,360.00×(1−0.15)=$3,360.00×0.85=$2,856.00\$3,360.00 \times (1 - 0.15) = \$3,360.00 \times 0.85 = \$2,856.00
The 15%15\% discount is taken off the standard retail price, not the original cost.
3
Calculate the final price including sales tax.
$2,856.00×1.06=$3,027.36\$2,856.00 \times 1.06 = \$3,027.36
Sales tax is calculated on the discounted sale price to find the total amount paid.

Key Concept

Calculating successive percentage changes (markups, discounts, and taxes) by updating the base value at each step.
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Topics

Percentage Change, Markups, and Discounts

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