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Question

Difficulty: MediumPercentage Calculations

A base exchange marks up the wholesale price of a standard watch by 20%20\% to determine its retail price. If the retail price of the watch is $150\$150, what was the original wholesale price and the markup amount? Complete the statement below with your calculated values.

Answer:The original wholesale price of the watch was 【125】 dollars, and the exact amount of the markup was 【25】 dollars.

Answer

The original wholesale price was 125 dollars, and the exact amount of the markup was 25 dollars.
Because the watch is marked up by 20%20\%, the $150\$150 retail price represents 120%120\% of the wholesale price. Dividing 150150 by 1.201.20 yields the correct wholesale price of 125125. The markup is the difference between the retail and wholesale prices (150−125=25150 - 125 = 25).

Step-by-Step Solution

1
Identify the mathematical relationship between the wholesale price, the markup percentage, and the retail price.
Wholesale Price+20% of Wholesale Price=Retail Price\text{Wholesale Price} + 20\% \text{ of Wholesale Price} = \text{Retail Price}
The markup is calculated based on the original wholesale price, not the final retail price.
2
Set up an algebraic equation where ww represents the wholesale price.
w+0.20w=$150w + 0.20w = \$150, which simplifies to 1.20w=$1501.20w = \$150
Translating the percentage relationship into a solvable equation allows us to find the unknown base amount.
3
Solve for the wholesale price (ww).
w=1501.20=125w = \frac{150}{1.20} = 125
Dividing the retail price by 1.201.20 isolates ww, giving the original wholesale price of $125\$125.
4
Calculate the exact markup amount by finding the difference between the retail and wholesale prices.
$150−$125=$25\$150 - \$125 = \$25
The markup amount is the portion added to the wholesale price to reach the retail price.

Key Concept

Reverse percentage calculation to find an original base amount.
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Topics

Percentage Calculations

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