A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day...

1. Translate the problem requirements: We need to find total gross profit, which is total revenue minus total cost. Given: 1500 cabbages bought for $600 total, 2/3 sold on day 1 at 25% markup, remaining 1/3 sold on day 2 at 10% less than day 1 price.
2. Establish baseline cost structure: Calculate the cost per head to establish our starting point for all subsequent pricing calculations.
3. Calculate day 1 sales impact: Determine quantity sold, selling price per head, and total revenue for the first day's sales at 25% markup.
4. Calculate day 2 sales impact: Determine quantity sold, selling price per head (10% less than day 1), and total revenue for the second day's sales.
5. Determine total gross profit: Sum both days' revenues and subtract total cost to find gross profit.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what we know in plain English. We have a business scenario where someone bought 1500 cabbages for a total of $600, then sold them over two days at different prices. We need to find the gross profit, which is simply how much more money they made from selling compared to what they originally paid.

Think of it like buying something and reselling it - your profit is the difference between what you sold it for and what you bought it for.

The selling happened in two parts:

• Day 1: 2/3 of the cabbages sold at 25% above cost per head
• Day 2: The remaining 1/3 sold at 10% less than the Day 1 price

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

2. Establish baseline cost structure

Before we can calculate any profits, we need to know how much each cabbage cost originally. This is our baseline for all other calculations.

Total cost = $600 for 1500 cabbages
Cost per cabbage = \(\$600 \div 1500 = \$0.40\) per head

So each cabbage cost 40 cents. This will be our reference point for calculating selling prices.

3. Calculate day 1 sales impact

On the first day, they sold 2/3 of the cabbages at a 25% markup above cost.

Quantity sold on Day 1: \(\frac{2}{3} \times 1500 = 1000\) cabbages

Now for the selling price. A 25% markup means they added 25% to the original cost:
Day 1 selling price = \(\$0.40 + (25\% \text{ of } \$0.40)\)
Day 1 selling price = \(\$0.40 + \$0.10 = \$0.50\) per head

Day 1 total revenue = \(1000 \text{ cabbages} \times \$0.50 = \$500\)

4. Calculate day 2 sales impact

The remaining cabbages were sold on Day 2. Let's figure out how many were left and at what price.

Quantity sold on Day 2: \(1500 - 1000 = 500\) cabbages

The Day 2 price was 10% less than the Day 1 price. So we take 10% off the $0.50 from Day 1:
Day 2 selling price = \(\$0.50 - (10\% \text{ of } \$0.50)\)
Day 2 selling price = \(\$0.50 - \$0.05 = \$0.45\) per head

Day 2 total revenue = \(500 \text{ cabbages} \times \$0.45 = \$225\)

5. Determine total gross profit

Now we can calculate the total gross profit by comparing total revenue to total cost.

Total revenue = Day 1 revenue + Day 2 revenue
Total revenue = \(\$500 + \$225 = \$725\)

Total cost = $600 (given)

Gross profit = Total revenue - Total cost
Gross profit = \(\$725 - \$600 = \$125\)

Final Answer

The gross profit on this shipment was $125, which matches answer choice (C).

Common Faltering Points

Errors while devising the approach

1. Misunderstanding what "gross profit" means: Students often confuse gross profit with profit margin or percentage profit. They might try to calculate a percentage instead of the absolute dollar difference between total revenue and total cost.

2. Misinterpreting the Day 2 pricing structure: The question states Day 2 price is "10% less than the price each head sold for the day before." Students may incorrectly think this means 10% less than the original cost per head ($0.40) rather than 10% less than the Day 1 selling price ($0.50).

3. Confusion about the reference point for markup calculations: When calculating the 25% markup for Day 1, students might mistakenly apply the 25% to the total cost ($600) or to the wrong base, rather than applying it to the cost per individual cabbage head ($0.40).

Errors while executing the approach

1. Arithmetic errors in fraction calculations: When calculating 2/3 of 1500 cabbages, students may make basic division errors or struggle with the fraction-to-whole number conversion, potentially getting 1000 wrong.

2. Percentage calculation mistakes: Students often make errors when calculating 25% of $0.40 or 10% of $0.50, either by using incorrect decimal conversions or by applying the percentage incorrectly (e.g., calculating \(\$0.40 \times 1.25\) instead of \(\$0.40 + (\$0.40 \times 0.25)\)).

3. Forgetting to account for all cabbages: Students may correctly calculate Day 1 sales but forget to calculate Day 2 sales, or vice versa, leading to incomplete revenue calculations.

Errors while selecting the answer

1. Selecting revenue instead of profit: After calculating the total revenue as $725, students might mistakenly select this as their final answer rather than subtracting the original cost of $600 to get the actual profit of $125.

2. Rounding errors leading to wrong answer choice: If students make small arithmetic errors during calculations, they might arrive at values like $120 or $130 and select the closest answer choice rather than recognizing their computational error.