A manufacturing plant makes 10-inch, 9-inch, and 7-inch frying pans. During a certain day, the number of 10-inch frying pans...

1. TRANSLATE the problem information

• Given information:
  • Let \(\mathrm{n}\) = number of 9-inch frying pans
  • Number of 10-inch pans = 4 times the number of 9-inch pans = \(\mathrm{4n}\)
  • Number of 7-inch pans = 10
  • Total pans made = 100

2. INFER the equation setup

• We need to account for all three types of pans
• The total must equal the sum of all individual pan types
• This gives us: 9-inch pans + 10-inch pans + 7-inch pans = Total pans

3. SIMPLIFY by combining terms

• Substitute our expressions: \(\mathrm{n + 4n + 10 = 100}\)
• Combine like terms: \(\mathrm{5n + 10 = 100}\)

Answer: D. \(\mathrm{5n + 10 = 100}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the pan sizes (10-inch, 9-inch, 7-inch) with coefficients in the algebraic equation.

Instead of recognizing that these numbers describe the physical size of the pans, they incorrectly use them as multipliers in their equation, creating something like \(\mathrm{10(4n) + 9n + 7(10) = 100}\).

This may lead them to select Choice A (\(\mathrm{10(4n) + 9n + 7(10) = 100}\))

Second Most Common Error:

Poor INFER reasoning: Students fail to account for the specific constraint that 10-inch pans are made "4 times" the number of 9-inch pans, instead treating all pan types as having equal variable representation.

This leads to equations like \(\mathrm{10n + 9n + 7n = 100}\), where each pan type gets the same variable treatment regardless of the given relationships.

This may lead them to select Choice B (\(\mathrm{10n + 9n + 7n = 100}\))

The Bottom Line:

This problem tests whether students can separate descriptive information (pan sizes) from quantitative relationships (how many of each type), then correctly translate those relationships into algebraic form.