A company's revenue was $95 million, which is $40 million more than its expenses. What were the expenses in millions...

1. TRANSLATE the problem information

• Given information:
  • Revenue = $95 million
  • Revenue is $40 million MORE than expenses

• What this tells us: \(\mathrm{Revenue = Expenses + \$40}\)

2. INFER the approach

• We need to find the expenses, so let's call expenses our unknown variable
• Since we know revenue and the relationship between revenue and expenses, we can set up an equation
• Our equation will be: \(\mathrm{Expenses + \$40 = \$95}\)

3. SIMPLIFY to solve for expenses

• \(\mathrm{Expenses + \$40 = \$95}\)
• Subtract $40 from both sides: \(\mathrm{Expenses = \$95 - \$40 = \$55}\)

Answer: C) 55

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "revenue is $40 million more than expenses" and think this means \(\mathrm{expenses = revenue + \$40}\), leading them to calculate \(\mathrm{\$95 + \$40 = \$135}\).

This may lead them to select Choice D (135).

Second Most Common Error:

Incomplete INFER reasoning: Students correctly understand that revenue is larger than expenses by $40, but then think the expenses must simply be the "$40 more" amount mentioned in the problem.

This may lead them to select Choice B (40).

The Bottom Line:

The key challenge is correctly translating the comparative language. "A is more than B" means A = B + (difference), not the other way around. Once you get the relationship right, the algebra is straightforward.