An account has an initial balance and grows at a constant rate. The equation b = 50 + 20t gives...

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{b = 50 + 20t}\) (balance b in dollars after t years)
  • Need balance "3 years after the initial deposit" → \(\mathrm{t = 3}\)

2. INFER the approach

• To find the balance after 3 years, substitute \(\mathrm{t = 3}\) into the equation
• This will give us the dollar amount in the account

3. SIMPLIFY by substituting and calculating

• Substitute \(\mathrm{t = 3}\): \(\mathrm{b = 50 + 20(3)}\)
• Follow order of operations - multiply first: \(\mathrm{b = 50 + 60}\)
• Add: \(\mathrm{b = 110}\)

Answer: C) 110

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors by not following proper order of operations or making basic calculation mistakes.

For example, they might calculate \(\mathrm{50 + 20 = 70}\) first (forgetting to multiply by 3), leading to an incorrect answer. This may lead them to select Choice B (70).

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly set up \(\mathrm{20(3) = 60}\) but forget to add the initial balance of 50.

They stop at just calculating the growth portion (60) without adding it to the starting amount. This may lead them to select Choice A (60).

The Bottom Line:

This problem tests whether students can accurately substitute values and perform multi-step arithmetic. The key is remembering that the equation has two parts: the initial balance (50) and the growth over time (20t).