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Difficulty: Very hardDiscounts and Sale Prices

A mechanic buys a new diagnostic tool for their shop. The tool is first marked down by 20%20\% for a storewide clearance. The mechanic then applies a special promotional code for an additional 15%15\% off the clearance price. Finally, a 6%6\% sales tax is applied to the discounted price.

If the total amount the mechanic paid, including the sales tax, was $864.96\$864.96, calculate the original price of the diagnostic tool before any discounts were applied.

Answer:The original price of the diagnostic tool was $【1200】\$【1200】.

Answer

The original price of the diagnostic tool was $1,200.
To find the original price, we must reverse each transaction step starting from the final price. First, we remove the 6%6\% sales tax by dividing $864.96\$864.96 by 1.061.06 to get $816.00\$816.00. Next, we reverse the 15%15\% discount by dividing $816.00\$816.00 by 0.850.85 (since the discounted price represents 85%85\% of the previous price), resulting in $960.00\$960.00. Finally, we reverse the 20%20\% clearance discount by dividing $960.00\$960.00 by 0.800.80, which yields the original price of $1,200.00\$1,200.00.

Step-by-Step Solution

1
Remove the 6%6\% sales tax from the final total to find the price of the tool after all discounts.
$864.96÷1.06=$816.00\$864.96 \div 1.06 = \$816.00
The final total represents 106%106\% of the discounted price. Dividing by 1.061.06 mathematically reverses the tax application.
2
Reverse the 15%15\% promotional discount to find the initial clearance price.
$816.00÷0.85=$960.00\$816.00 \div 0.85 = \$960.00
The price after the promo code was applied represents 85%85\% (100%−15%100\% - 15\%) of the clearance price. Dividing by 0.850.85 finds the value before this second discount.
3
Reverse the initial 20%20\% clearance markdown to determine the original price.
$960.00÷0.80=$1,200.00\$960.00 \div 0.80 = \$1,200.00
The clearance price represents 80%80\% (100%−20%100\% - 20\%) of the original price. Dividing by 0.800.80 finds the starting value.

Key Concept

Reversing successive percentage changes (chain discounts and taxes) using inverse operations to find an original value.
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Topics

Discounts and Sale Prices

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