A restaurant analyzed 240 randomly selected customer orders from their database. They found that 144 customers ordered meat dishes, 72...

1. TRANSLATE the problem information

• Given information:
  • Sample size: 240 customers
  • Meat dishes: 144 customers
  • Vegetarian dishes: 72 customers
  • Vegan dishes: 24 customers
  • Target population: 1,200 customers

• What we need to find: How many MORE customers will order meat than the combined vegetarian + vegan orders

2. INFER the solution approach

• This is a proportional reasoning problem - we use sample proportions to predict population behavior
• Strategy: Find sample proportions → Scale to population → Calculate difference
• We need to combine vegetarian and vegan into one category since the question asks for their total

3. SIMPLIFY the sample proportions

• Meat proportion: \(\frac{144}{240} = 0.6\) (or 60%)
• Combined vegetarian + vegan: \(\frac{72 + 24}{240} = \frac{96}{240} = 0.4\) (or 40%)

4. SIMPLIFY the population predictions

• Expected meat orders: \(0.6 \times 1,200 = 720\) customers
• Expected vegetarian + vegan orders: \(0.4 \times 1,200 = 480\) customers

5. SIMPLIFY the final calculation

• Difference: \(720 - 480 = 240\) more customers

Answer: B (240)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students miss that the question asks for "how many MORE" and instead calculate just the number of meat orders (720) or just the vegetarian + vegan orders (480).

They correctly find the proportions and scale them up, but then stop without calculating the difference. This may lead them to select Choice D (720) if they report just the meat orders.

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when combining the vegetarian and vegan categories or when scaling the proportions to 1,200 customers.

For example, they might forget to add \(72 + 24 = 96\) before finding the proportion, or make multiplication errors when scaling. This leads to confusion and guessing among the remaining answer choices.

The Bottom Line:

This problem tests whether students can maintain focus on the specific question being asked while executing a multi-step proportional reasoning process. The key challenge is remembering that "how many more" requires a subtraction step at the end.