A car is filled with four and a half gallons of fuel for a round trip. If the amount of fuel taken while going is $\frac{1}{4}$ more than the amount taken for coming, what is the amount of fuel consumed while coming back?
(a)Less than 2 gallons
(b)2 gallons
(c)$2 \frac{1}{2}$ gallons
(d)3 gallons
(e)More than 3 gallons
Answer
Answer (as printed): B
Explanation
Let the amount of fuel consumed while coming back be $x$ gallons. Then, amount of fuel consumed while going $$\begin{aligned} & =\left(x+\frac{x}{4}\right) \text { gallons }=\frac{5 x}{4} \text { gallons. } \\ & \therefore \quad x+\frac{5 x}{4}=4 \frac{1}{2} \Leftrightarrow \frac{9 x}{4}=\frac{9}{2} \Leftrightarrow x=\frac{9}{2} \times \frac{4}{9}=2 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.