4x + 3y = 24Mario purchased 4 binders that cost x dollars each and 3 notebooks that cost y dollars...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{4x + 3y = 24}\)
  • Mario bought 4 binders at \(\mathrm{x}\) dollars each
  • Mario bought 3 notebooks at \(\mathrm{y}\) dollars each

• What this tells us:
  • \(\mathrm{4x}\) = total cost of all binders (4 items × \(\mathrm{x}\) dollars each)
  • \(\mathrm{3y}\) = total cost of all notebooks (3 items × \(\mathrm{y}\) dollars each)

2. INFER what the equation means

• Since \(\mathrm{4x}\) represents all binder costs and \(\mathrm{3y}\) represents all notebook costs:
  • \(\mathrm{4x + 3y}\) represents the total cost of everything Mario bought
  • The equation tells us this total equals 24

• Therefore: 24 represents the total cost of all binders and notebooks combined

Answer: C. The total cost, in dollars, for all binders and notebooks purchased

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students focus on individual parts of the equation without connecting them to the complete picture.

They might see "\(\mathrm{4x}\)" and think "24 must be the cost of binders" or see "\(\mathrm{3y}\)" and think "24 must be the cost of notebooks." They don't recognize that 24 equals the entire left side of the equation (\(\mathrm{4x + 3y}\)), not just one part.

This may lead them to select Choice A (cost of binders only) or Choice B (cost of notebooks only).

The Bottom Line:

This problem tests whether students can connect algebraic expressions to their real-world meaning. The key insight is recognizing that 24 represents whatever the entire expression \(\mathrm{4x + 3y}\) represents - not just individual pieces of it.