F = 2.50x + 7.00yIn the equation above, F represents the total amount of money, in dollars, a food truck...

1. TRANSLATE the problem information

• Given equation: \(\mathrm{F = 2.50x + 7.00y}\)
• Given facts:
  • \(\mathrm{F}\) = total money charged (dollars)
  • \(\mathrm{x}\) = number of drinks purchased
  • \(\mathrm{y}\) = number of salads purchased
  • Each drink has the same price
  • Each salad has the same price

2. INFER the equation structure

• This is a linear cost equation with the pattern:
  \(\mathrm{Total\ Cost = (price\ per\ drink)(number\ of\ drinks) + (price\ per\ salad)(number\ of\ salads)}\)
• In general form: \(\mathrm{F = (price_1)x + (price_2)y}\)
• The coefficients (2.50 and 7.00) must represent the unit prices

3. INFER what each coefficient represents

• Comparing \(\mathrm{F = 2.50x + 7.00y}\) with \(\mathrm{F = (price\ per\ drink)x + (price\ per\ salad)y}\):
  • \(\mathrm{2.50 = price\ per\ drink}\)
  • \(\mathrm{7.00 = price\ per\ salad}\)

4. Verify with substitution

• If we buy 1 salad (\(\mathrm{y = 1}\)), the salad cost contribution is:
  \(\mathrm{7.00(1) = \$7.00}\)
• This confirms 7.00 is the price of one salad

Answer: B. The price, in dollars, of one salad

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not recognize the standard structure of linear cost equations, treating the coefficients as arbitrary numbers rather than meaningful unit prices.

Without understanding that coefficients represent "price per item" when multiplied by quantities, students may randomly guess or confuse which coefficient goes with which item type. This may lead them to select Choice A (The price, in dollars, of one drink) by incorrectly associating 7.00 with drinks instead of salads.

Second Most Common Error:

TRANSLATE confusion about variables vs. coefficients: Students may think the numbers 2.50 and 7.00 represent quantities (how many items) rather than prices (cost per item).

This conceptual mix-up between what represents "how many" versus "how much each costs" may lead them to select Choice C or D (thinking 7.00 represents the number of items sold during the day).

The Bottom Line:

Success requires recognizing that linear cost equations follow the pattern "Total = (unit price × quantity) + (unit price × quantity)" where the coefficients are always the unit prices, not the quantities.