Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of...

1. TRANSLATE the problem information

• Given information:
  • Each serving of cereal provides \(5\%\) of an adult's daily potassium allowance
  • We want to find p percent (the total percentage) provided by x servings

• What this tells us: We need to find how multiple servings combine

2. INFER the scaling relationship

• Key insight: Multiple identical servings provide a total that scales linearly
• If 1 serving gives \(5\%\), then 2 servings give \(2 \times 5\% = 10\%\)
• Therefore, x servings give \(x \times 5\% = 5x\%\)

3. TRANSLATE to final mathematical expression

• Since p represents the percentage of daily allowance from x servings:
• \(\mathrm{p = 5x}\)

Answer: B. p = 5x

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students incorrectly convert \(5\%\) to its decimal equivalent \(0.05\) and think the answer should involve \(0.05\), not recognizing that p is expressed as a percentage.

This confusion might lead them to look for answers involving \(0.05\), potentially causing them to select Choice A (\(\mathrm{p = 0.5x}\)) after making additional conversion errors, or get confused and guess.

Second Most Common Error:

Poor INFER reasoning: Students incorrectly think that consuming multiple servings creates some kind of exponential or compound effect rather than simple linear addition.

This fundamental misunderstanding of how quantities combine may lead them to select Choice C (\(\mathrm{p = (0.05)^x}\)) or Choice D (\(\mathrm{p = (1.05)^x}\)), thinking the relationship involves exponential growth.

The Bottom Line:

This problem tests whether students understand that identical quantities scale linearly and whether they can keep track of percentage vs. decimal representations. The key insight is recognizing that nutrition facts simply add up - there's no compound effect when eating multiple servings.