A merchant bought a coat at a wholesale price of $120 and then sold it at a 20 percent discount...

1. Translate the problem requirements: The merchant bought a coat for $120 (wholesale price), sold it at 20% discount off regular price, and made 40% profit on the wholesale price. We need to find the original regular retail price before the discount.
2. Calculate the actual selling price using profit information: Since the merchant made 40% profit on the $120 wholesale price, determine what price the coat was actually sold for.
3. Connect selling price to regular price through discount relationship: The selling price represents 80% of the regular price (since there was a 20% discount), so use this relationship to find the regular price.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what we know from the problem in everyday language:

• The merchant bought a coat for $120 - this is what we call the wholesale price (what the merchant paid)
• The merchant sold the coat at a 20% discount off the regular price - this means customers paid less than the original sticker price
• The merchant made a 40% profit on the wholesale price - this means the merchant earned 40% more than the $120 they originally paid
• We need to find the regular retail price - this is the original sticker price before any discount was applied

Think of it this way: there are three different prices in this story - the wholesale price ($120), the regular retail price (what we're looking for), and the actual selling price (what customers actually paid after the discount).

Process Skill: TRANSLATE - Converting the problem language into clear mathematical relationships

2. Calculate the actual selling price using profit information

Since the merchant made a 40% profit on the $120 wholesale price, let's figure out what price the coat was actually sold for.

In plain English: if you make a 40% profit, you get back your original money plus 40% extra. So the merchant received back the original $120 plus 40% of $120.

\(40\% \text{ of } \$120 = 0.40 \times \$120 = \$48\)

So the actual selling price = \(\$120 + \$48 = \$168\)

This $168 is what customers actually paid for the coat after the 20% discount was applied.

3. Connect selling price to regular price through discount relationship

Now here's the key insight: the $168 that customers paid represents the regular price after a 20% discount was taken off.

In everyday terms: if something is discounted by 20%, then customers pay 80% of the original price. Think of it like this - if the regular price is 100%, and you take away 20%, you're left with 80%.

So we can say: $168 represents 80% of the regular price.

To find the regular price, we need to figure out: if 80% equals $168, what does 100% equal?

Let's call the regular price R.

\(80\% \text{ of } R = \$168\)

\(0.80 \times R = \$168\)

\(R = \$168 \div 0.80\)

\(R = \$210\)

Process Skill: INFER - Recognizing that the selling price after discount represents 80% of the regular price

4. Final Answer

The regular retail price of the coat was $210.

Let's verify this makes sense:

• Regular price: $210
• 20% discount: \(20\% \text{ of } \$210 = \$42\)
• Selling price: \(\$210 - \$42 = \$168\) ✓
• Profit: \(\$168 - \$120 = \$48\)
• Profit percentage: \(\$48 \div \$120 = 0.40 = 40\%\) ✓

The answer is D. $210

Common Faltering Points

Errors while devising the approach

1. Confusing the three different prices in the problem
Students often struggle to distinguish between wholesale price ($120), regular retail price (unknown), and actual selling price (what customers paid). They might mistakenly think the regular price is $120 or confuse which price the 20% discount applies to.

2. Misinterpreting what "40% profit on wholesale price" means
Students may think 40% profit means the selling price is 40% of the wholesale price (which would be $48) rather than understanding it means the selling price is 140% of the wholesale price (original cost plus 40% extra).

3. Not recognizing the relationship between discount and percentage paid
Students often fail to realize that a 20% discount means customers pay 80% of the regular price. They might try to add 20% to the selling price instead of understanding the inverse relationship.

Errors while executing the approach

1. Arithmetic errors in percentage calculations
Students might incorrectly calculate 40% of $120 (getting values other than $48) or make errors when adding $120 + $48 to get the selling price.

2. Division errors when finding the regular price
When solving 0.80 × R = $168, students might incorrectly multiply $168 by 0.80 instead of dividing by 0.80, or make computational errors in $168 ÷ 0.80.

3. Using incorrect percentage conversions
Students might use 20% (0.20) instead of 80% (0.80) when setting up the equation, or confuse which percentage to use in their calculations.

Errors while selecting the answer

1. Selecting the selling price instead of the regular price
After correctly calculating that the selling price is $168, students might mistakenly select answer choice B ($168) instead of continuing to find the regular retail price of $210.