A batch of banana milkshakes consists of 4 cups of ice cream and 2 bananas and has 1,114 milligrams (mg)...

1. TRANSLATE the problem information

• Given information:
  • Batch = 4 cups ice cream + 2 bananas
  • Total calcium in batch = 1,114 mg
  • Calcium per cup ice cream = 276 mg
  • Want: calcium in 1 banana

2. INFER the approach

• Strategy: Find total calcium from ice cream first, then subtract from batch total to find banana contribution
• This works because: Total calcium = Ice cream calcium + Banana calcium

3. SIMPLIFY to find ice cream calcium

• Calcium from ice cream = \(4 \times 276 = 1,104\) mg

4. SIMPLIFY to find total banana calcium

• Calcium from bananas = Total batch calcium - Ice cream calcium
• Calcium from bananas = \(1,114 - 1,104 = 10\) mg
• This 10 mg is for 2 bananas combined

5. SIMPLIFY to find calcium per banana

• Calcium per banana = Total banana calcium ÷ 2 bananas
• Calcium per banana = \(10 \div 2 = 5\) mg

Answer: A. 5

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly set up the problem but stop after finding the total calcium from bananas (10 mg) and forget to divide by 2 to get the per-banana amount.

They get 1,114 - 1,104 = 10 and think they're done, not realizing this represents 2 bananas.

This leads them to select Choice B (10).

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up which values go where in their calculations or misread what the problem is asking for.

Some students might accidentally use 1,104 mg (the ice cream total) as their final answer, thinking this somehow represents banana calcium.

This may lead them to select Choice D (1,104).

The Bottom Line:

This problem tests whether students can systematically work backwards from a total to find individual components. The key insight is recognizing that you must account for all parts of the mixture and remember that the banana calcium found represents multiple bananas.