The function \(\mathrm{f(x) = 45x + 600}\) gives the monthly fee \(\mathrm{f(x)}\), in dollars, a facility charges to keep x...

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = 45x + 600}\) (monthly fee in dollars for storing x crates)
  • Need to find: monthly fee for storing 50 crates
• What this tells us: We need to find \(\mathrm{f(50)}\)

2. INFER the approach

• To evaluate a function at a specific input value, substitute that value for the variable
• Since we want \(\mathrm{f(50)}\), we substitute \(\mathrm{x = 50}\) into \(\mathrm{f(x) = 45x + 600}\)

3. SIMPLIFY the calculation

• \(\mathrm{f(50) = 45(50) + 600}\)
• \(\mathrm{f(50) = 2250 + 600}\)
• \(\mathrm{f(50) = 2850}\)

Answer: 2850

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not recognize that "monthly fee for 50 crates" translates to \(\mathrm{f(50)}\). They might try to solve for x when \(\mathrm{f(x) = 50}\), or get confused about what the problem is actually asking for. This leads to confusion and guessing rather than systematic solution.

Second Most Common Error:

Poor SIMPLIFY execution: Students understand they need to calculate \(\mathrm{f(50) = 45(50) + 600}\), but make arithmetic errors, such as calculating \(\mathrm{45 \times 50 = 2500}\) instead of 2250, leading to \(\mathrm{f(50) = 3100}\) instead of 2850.

The Bottom Line:

This problem tests whether students truly understand function notation and can translate real-world language into mathematical operations. The calculation itself is straightforward once students recognize what they need to find.