A nutritionist recommends that Maya consume at least 60 grams of protein daily. Each serving of chicken contains 8 grams...

1. TRANSLATE the problem information

• Given information:
  • Maya needs at least 60 grams of protein daily
  • Each serving of chicken = 8 grams of protein
  • Each serving of beans = 12 grams of protein
  • \(\mathrm{c}\) = number of chicken servings, \(\mathrm{b}\) = number of bean servings

• Key phrase: "at least 60 grams" means \(\geq 60\)

2. INFER the total protein calculation

• Total protein intake = protein from chicken + protein from beans
• From \(\mathrm{c}\) servings of chicken: \(8\mathrm{c}\) grams
• From \(\mathrm{b}\) servings of beans: \(12\mathrm{b}\) grams
• Therefore: Total protein = \(8\mathrm{c} + 12\mathrm{b}\) grams

3. TRANSLATE the constraint into mathematical form

• "Maya must consume at least 60 grams" becomes:
• \(8\mathrm{c} + 12\mathrm{b} \geq 60\)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students mix up which food provides how much protein, writing \(12\mathrm{c} + 8\mathrm{b}\) instead of \(8\mathrm{c} + 12\mathrm{b}\).

They might quickly scan and associate the first number (12) with the first variable (\(\mathrm{c}\)), leading to the reversed coefficients. This systematic misreading of the problem setup leads them to select Choice C (\(12\mathrm{c} + 8\mathrm{b} \geq 60\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse "at least" with "at most," thinking Maya should limit her protein intake rather than meet a minimum requirement.

This conceptual misunderstanding of the constraint language makes them flip the inequality direction, leading them to select Choice B (\(8\mathrm{c} + 12\mathrm{b} \leq 60\)).

The Bottom Line:

This problem tests whether students can carefully match numerical information with the correct variables and properly translate constraint language ("at least") into mathematical inequalities. The key is methodical translation rather than speed.