A shipping company processes packages with a total weight of 378 pounds. The equation 18x + 29y = 378 represents...

1. TRANSLATE the equation information

• Given equation: \(\mathrm{18x + 29y = 378}\)
• Where:
  • x = number of standard packages
  • y = number of express packages
  • 378 = total weight in pounds
• What this tells us: The coefficient of each variable represents the weight of that type of package
  • 18 = weight of each standard package (in pounds)
  • 29 = weight of each express package (in pounds)

2. INFER what the question asks for

• Question: 'How many more pounds does each express package weigh than each standard package?'
• This means we need to find: Express package weight - Standard package weight

3. SIMPLIFY the calculation

• Difference = \(\mathrm{29 - 18 = 11}\) pounds

Answer: A) 11

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students see the coefficients 18 and 29 but don't connect them to individual package weights. Instead, they might think these numbers represent something else about the equation or that one of them IS the final answer.

This may lead them to select Choice B (18) or Choice C (29) thinking the answer is simply one of the coefficient values.

Second Most Common Error:

Poor INFER reasoning: Students correctly identify what 18 and 29 represent but misunderstand what 'how many more' means. They might think they need to add the weights together instead of finding the difference.

This may lead them to select Choice D (47) since \(\mathrm{18 + 29 = 47}\).

The Bottom Line:

This problem tests whether students can interpret coefficients in context and understand what mathematical operation corresponds to 'how many more.' The equation itself doesn't need to be solved - you just need to understand what its parts represent.