A food truck buys forks for $0.04 each and plates for $0.48 each. The total cost of x forks and...

1. TRANSLATE the cost information

• Given information:
  • Forks cost \(\$0.04\) each, and we buy x forks
  • Plates cost \(\$0.48\) each, and we buy y plates
  • Total spent is \(\$661.76\)

• This translates to:
  • Cost of x forks = \(\$0.04 \times \mathrm{x} = 0.04\mathrm{x}\)
  • Cost of y plates = \(\$0.48 \times \mathrm{y} = 0.48\mathrm{y}\)

2. INFER how to represent total cost

• The total cost is the sum of money spent on both items
• Total cost = cost of forks + cost of plates
• So: Total cost = \(0.04\mathrm{x} + 0.48\mathrm{y}\)

3. Set up the equation

• Since the total cost equals \(\$661.76\):

\(0.04\mathrm{x} + 0.48\mathrm{y} = 661.76\)

Answer: D. \(0.04\mathrm{x} + 0.48\mathrm{y} = 661.76\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students mix up which cost goes with which variable, confusing the unit costs of \(\$0.04\) and \(\$0.48\).

They might think "x comes first in the alphabet, so it should get the first number mentioned" or get confused about which item costs what amount. This leads them to write \(0.48\mathrm{x} + 0.04\mathrm{y}\) instead of \(0.04\mathrm{x} + 0.48\mathrm{y}\).

This may lead them to select Choice C (\(0.48\mathrm{x} + 0.04\mathrm{y} = 661.76\)).

Second Most Common Error:

Poor INFER reasoning: Students don't recognize that "total cost" means adding the individual costs together.

They might think there's some subtraction involved or that costs work differently, leading them to consider equations with minus signs between the terms.

This may lead them to select Choice A (\(0.48\mathrm{x} - 0.04\mathrm{y} = 661.76\)) or Choice B (\(0.04\mathrm{x} - 0.48\mathrm{y} = 661.76\)).

The Bottom Line:

Success requires carefully matching each item with its unit cost and understanding that total cost means adding up all individual costs. The key is staying organized about which number goes with which variable.