The speed of sound in dry air, v, can be modeled by the formula v = 331.3 + 0.606T, where...

1. TRANSLATE the problem requirement

• Given: \(\mathrm{v = 331.3 + 0.606T}\)
• Need to find: T in terms of v (isolate T on one side)

2. INFER the algebraic strategy

• T is currently on the right side with two operations applied: +331.3 and ×0.606
• To isolate T, undo these operations in reverse order:
  • First: subtract 331.3 from both sides
  • Second: divide both sides by 0.606

3. SIMPLIFY by subtracting 331.3 from both sides

\(\mathrm{v = 331.3 + 0.606T}\)

\(\mathrm{v - 331.3 = 0.606T}\)

4. SIMPLIFY by dividing both sides by 0.606

\(\mathrm{T = \frac{v - 331.3}{0.606}}\)

Answer: D. \(\mathrm{T = \frac{v - 331.3}{0.606}}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students reverse the order of operations incorrectly, thinking they should divide first, then subtract. This leads them to manipulate the equation as: \(\mathrm{\frac{v}{0.606} = 331.3 + T}\), then \(\mathrm{T = \frac{v}{0.606} - 331.3}\), which doesn't match any answer choice exactly and causes confusion.

Second Most Common Error:

Poor SIMPLIFY execution: Students make sign errors when moving terms across the equals sign. Instead of subtracting 331.3 from both sides, they add 331.3, getting: \(\mathrm{v + 331.3 = 0.606T}\), then \(\mathrm{T = \frac{v + 331.3}{0.606}}\). This may lead them to select Choice C (\(\mathrm{\frac{v + 331.3}{0.606}}\)).

The Bottom Line:

This problem tests whether students can systematically undo operations in the correct order when solving for a variable. The key insight is recognizing that to isolate T, you must reverse the order in which operations were originally applied.