Examkin

Soru

Zorluk: Çok zorDiscounts 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.

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

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Konular

Discounts and Sale Prices

Bu konudan daha fazla soru