The formula \(\mathrm{T = B + \frac{4}{9}(225 - H)}\) can be used to calculate the adjusted temperature T, in degrees...

1. INFER the problem goal

• Given: \(\mathrm{T = B + \frac{4}{9}(225 - H)}\)
• Goal: Solve for H in terms of T and B
• Strategy: Use algebraic manipulation to isolate H

2. SIMPLIFY by eliminating B from the right side

• Subtract B from both sides: \(\mathrm{T - B = \frac{4}{9}(225 - H)}\)
• This isolates the term containing H

3. SIMPLIFY by eliminating the fraction

• Multiply both sides by 9/4: \(\mathrm{\frac{9}{4}(T - B) = 225 - H}\)
• Now H appears without a fraction coefficient

4. SIMPLIFY by isolating H

• Rearrange: \(\mathrm{H = 225 - \frac{9}{4}(T - B)}\)
• H is now isolated, but we need to clean up the expression

5. SIMPLIFY the final expression

• Distribute the negative: \(\mathrm{H = 225 + \frac{9}{4}(B - T)}\)
• Reorder: \(\mathrm{H = \frac{9}{4}(B - T) + 225}\)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Sign errors when distributing the negative sign

When going from \(\mathrm{H = 225 - \frac{9}{4}(T - B)}\) to the final form, students often incorrectly distribute the negative, getting \(\mathrm{H = \frac{9}{4}(B - T) - 225}\) instead of \(\mathrm{H = \frac{9}{4}(B - T) + 225}\).

This may lead them to select Choice B (\(\mathrm{H = \frac{9}{4}(B - T) - 225}\))

Second Most Common Error:

Poor SIMPLIFY reasoning: Algebraic manipulation mistakes in middle steps

Students might make errors when multiplying by 9/4 or when rearranging terms, leading to incorrect signs within the parentheses. This creates confusion about whether it should be (B - T) or (B + T).

This may lead them to select Choice C (\(\mathrm{H = \frac{9}{4}(B + T) + 225}\)) or causes them to get stuck and guess

The Bottom Line:

This problem tests systematic algebraic manipulation skills. Success depends on carefully tracking signs through multiple steps, especially when distributing negative signs and rearranging terms.