FoodProteinCost1 large egg6text{ grams}$0.361 cup of milk8text{ grams}$0.24The table above shows the amount of protein in two foods and the...

1. TRANSLATE the problem requirements

• Given information:
  • Large egg: \(6\mathrm{g}\) protein, \(\$0.36\)
  • Cup of milk: \(8\mathrm{g}\) protein, \(\$0.24\)
• Need to find: Ratio of (cost per gram protein in egg) to (cost per gram protein in milk)

2. INFER the solution approach

• The problem asks for a ratio between two unit rates
• We must calculate each unit rate first: cost ÷ grams = cost per gram
• Then form the ratio in the specified order (egg to milk)

3. Calculate the unit rates

• Cost per gram of protein in egg: \(\$0.36 \div 6 = \$0.06\) per gram
• Cost per gram of protein in milk: \(\$0.24 \div 8 = \$0.03\) per gram

4. SIMPLIFY by forming and reducing the ratio

• Ratio = \(\$0.06 : \$0.03\)
• Divide both parts by \(\$0.03\): \(2 : 1\)

Answer: D. \(2 : 1\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misread the problem and calculate the ratio in reverse order (milk to egg instead of egg to milk).

They correctly find the unit rates (\(\$0.06\) for egg, \(\$0.03\) for milk) but then write the ratio as \(\$0.03 : \$0.06 = 1 : 2\). This may lead them to select Choice A (\(1 : 2\)).

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when calculating the unit rates, such as \(\$0.36 \div 6 = \$0.04\) or \(\$0.24 \div 8 = \$0.04\).

These calculation errors lead to incorrect ratios that don't match any systematic pattern. This causes them to get stuck and randomly select an answer.

The Bottom Line:

This problem requires careful attention to the order specified in the ratio and accurate calculation of unit rates. Success depends on systematically working through each unit rate calculation before forming the final ratio.