A gym requires members to earn at least 50 fitness points per week through cardio and strength training activities. Cardio...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{6x + 9y \geq 50}\) is the inequality
  • \(\mathrm{x}\) = number of cardio sessions
  • \(\mathrm{y}\) = number of strength training sessions
  • Cardio sessions = 6 points each
  • Strength training sessions = 9 points each

2. TRANSLATE what each part of 9y means

• In the term \(\mathrm{9y}\):
  • 9 is the coefficient = points earned per strength training session
  • y is the variable = number of strength training sessions

3. INFER the meaning of the complete expression

• When we multiply: \(\mathrm{9 \times y}\) = (points per session) × (number of sessions)
• This gives us the total points earned from all strength training sessions combined
• So \(\mathrm{9y}\) represents the total number of points earned from strength training sessions

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the coefficient (per-session rate) with the entire expression (total points).

They see "9" in the expression \(\mathrm{9y}\) and think it represents the total points, leading them to select Choice B (The number of points earned from each strength training session) when they should recognize that \(\mathrm{9y}\) as a whole represents the total.

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up cardio and strength training terms.

They associate the wrong coefficient with the wrong activity type, thinking \(\mathrm{9y}\) relates to cardio instead of strength training. This leads them to select Choice D (The total number of points earned from cardio sessions).

The Bottom Line:

Success requires carefully translating each component of an algebraic expression back to its real-world meaning, recognizing that coefficient × variable gives a total quantity, not just the rate.