An employee at a restaurant prepares sandwiches and salads. It takes the employee 1.5 minutes to prepare a sandwich and...

1. TRANSLATE the problem information

• Given information:
  • 1.5 minutes to prepare each sandwich
  • 1.9 minutes to prepare each salad
  • x sandwiches prepared
  • y salads prepared
  • Total preparation time = 46.1 minutes

2. TRANSLATE each part into mathematical expressions

• Time spent on sandwiches: 1.5 minutes per sandwich × x sandwiches = \(\mathrm{1.5x}\) minutes
• Time spent on salads: 1.9 minutes per salad × y salads = \(\mathrm{1.9y}\) minutes

3. INFER the relationship for total time

• Total time = time for sandwiches + time for salads
• Therefore: \(\mathrm{1.5x + 1.9y = 46.1}\)

4. Match with answer choices

• The equation \(\mathrm{1.5x + 1.9y = 46.1}\) corresponds to Choice B

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students mix up which coefficient goes with which variable, thinking "1.5 minutes for a sandwich" means the coefficient 1.5 should go with y (salads) instead of x (sandwiches).

This backwards thinking leads to the equation \(\mathrm{1.9x + 1.5y = 46.1}\), causing them to select Choice A (\(\mathrm{1.9x + 1.5y = 46.1}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students recognize they need an equation but oversimplify by ignoring the different preparation times, thinking the total is just the sum of the quantities.

This leads them to write \(\mathrm{x + y = 46.1}\) and select Choice C (\(\mathrm{x + y = 46.1}\)).

The Bottom Line:

Success requires carefully tracking which time corresponds to which food item and translating "rate × quantity" relationships accurately into algebraic expressions.