The fuel efficiency of a certain vehicle, E, can be modeled by the formula E = 44.8 - 0.8S, where...

1. TRANSLATE the problem requirements

• Given: \(\mathrm{E = 44.8 - 0.8S}\)
• Need to find: \(\mathrm{S}\) in terms of \(\mathrm{E}\) (isolate \(\mathrm{S}\))

2. SIMPLIFY by isolating the term with S

• Subtract 44.8 from both sides:

\(\mathrm{E - 44.8 = 44.8 - 0.8S - 44.8}\)

\(\mathrm{E - 44.8 = -0.8S}\)

3. SIMPLIFY by solving for S

• Divide both sides by -0.8:

\(\mathrm{S = \frac{E - 44.8}{-0.8}}\)

4. SIMPLIFY the final expression

• Factor out the negative sign:

\(\mathrm{S = -\frac{E - 44.8}{0.8}}\)

\(\mathrm{S = \frac{-E + 44.8}{0.8}}\)

\(\mathrm{S = \frac{44.8 - E}{0.8}}\)

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Incorrectly handling negative signs during algebraic manipulation

When dividing \(\mathrm{(E - 44.8)}\) by \(\mathrm{(-0.8)}\), students often forget to properly distribute the negative sign, leading them to write \(\mathrm{S = \frac{E - 44.8}{0.8}}\) instead of the correct \(\mathrm{S = \frac{44.8 - E}{0.8}}\).

This may lead them to select Choice A: \(\mathrm{\frac{E - 44.8}{0.8}}\)

Second Most Common Error:

Poor SIMPLIFY execution: Making sign errors in the initial step

Students might incorrectly add 44.8 to both sides instead of subtracting, or make other early algebraic mistakes that propagate through the solution.

This may lead them to select Choice B: \(\mathrm{\frac{E + 44.8}{0.8}}\)

The Bottom Line:

This problem tests careful algebraic manipulation, particularly with negative coefficients. The key challenge is maintaining accuracy with signs throughout multiple algebraic steps.