- Translate the problem requirements: We need to find the store's profit as a percentage of the original retail price. The store bought at $60, sold at 40% discount off retail price, and made 25% profit on wholesale cost.
- Calculate the actual selling price using profit information: Since the store made 25% profit on $60 wholesale cost, determine what they actually sold the CD player for.
- Work backwards to find the original retail price: Use the fact that the selling price represents 60% of the original retail price (since it was sold at 40% discount).
- Calculate profit as percentage of retail price: Find the difference between selling price and wholesale cost, then express this profit as a percentage of the original retail price.
Execution of Strategic Approach
1. Translate the problem requirements
Let's break down what we know in everyday language:
- The store bought a CD player for $60 (this is the wholesale price)
- They sold it at a 40% discount off some original retail price
- Despite the discount, they still made a 25% profit on their $60 cost
- We need to find: what percentage of the original retail price was their profit?
Process Skill: TRANSLATE - Converting the problem's business language into clear mathematical relationships
2. Calculate the actual selling price using profit information
Since the store made a 25% profit on their $60 wholesale cost, let's figure out what they actually sold the CD player for.
In plain English: If they made 25% profit on $60, that means they earned an extra $15 on top of their $60 cost.
Profit = 25% of $60 = \(0.25 \times \$60 = \$15\)
So the actual selling price = Cost + Profit = \(\$60 + \$15 = \$75\)
This means the customer paid $75 for the CD player.
3. Work backwards to find the original retail price
Now here's the key insight: that $75 selling price represents the original retail price AFTER a 40% discount was applied.
In everyday terms: If someone got 40% off, they paid 60% of the original price.
So $75 represents 60% of the original retail price.
Let's call the original retail price R.
\(60\% \text{ of } R = \$75\)
\(0.6 \times R = \$75\)
\(R = \$75 \div 0.6 = \$125\)
So the original retail price was $125.
Process Skill: INFER - Recognizing that the discounted price allows us to work backwards to find the original retail price
4. Calculate profit as percentage of retail price
Now we can answer the question. We know:
- Wholesale cost: $60
- Selling price: $75
- Original retail price: $125
The store's profit = Selling price - Wholesale cost = \(\$75 - \$60 = \$15\)
Profit as a percentage of the original retail price = \((\$15 \div \$125) \times 100\%\)
= \(0.12 \times 100\% = 12\%\)
Final Answer
The store's profit as a percent of the original retail price is 12%.
Let's verify: The store made $15 profit on a CD player that had an original retail price of $125. Indeed, \(\$15/\$125 = 0.12 = 12\%\).
The answer is B. 12%
Common Faltering Points
Errors while devising the approach
- Confusing what the final answer should represent: Students often misread the question and think they need to find the profit as a percentage of the wholesale price (which would be 25%) or as a percentage of the selling price, rather than as a percentage of the original retail price. This leads them down the wrong path from the start.
- Not recognizing the need to find the original retail price first: Many students try to directly calculate percentages without realizing they need to work backwards from the discounted selling price to determine what the original retail price was. They might attempt to use the wholesale price as their base instead.
- Misunderstanding the discount relationship: Students may incorrectly think that if there's a 40% discount, the selling price is 40% of the original price, when it's actually 60% (100% - 40%) of the original price.
Errors while executing the approach
- Arithmetic errors when calculating the original retail price: When working backwards from the 60% equation (0.6 × R = $75), students commonly make division errors, calculating $75 ÷ 0.6 incorrectly. Some might get $112.50 instead of $125, or other incorrect values.
- Using wrong percentage calculations: Students might incorrectly calculate 25% of $60 as something other than $15, or make errors when converting between decimals and percentages (like using 0.025 instead of 0.25 for 25%).
- Mixing up the profit calculation: Some students might subtract in the wrong order (wholesale price minus selling price) or forget to subtract at all, leading to incorrect profit amounts.
Errors while selecting the answer
- Selecting an intermediate calculation as the final answer: Students might see the 25% profit margin and select 20% or 18% thinking they need to adjust it somehow, rather than completing the full calculation to get 12%.
- Converting decimal to percentage incorrectly: After correctly calculating 0.12, some students might convert this to 1.2% instead of 12%, or make other conversion errors when expressing their final answer as a percentage.
