A tree grows only $\frac{3}{5}$ as fast as the one beside it. In four years the combined growth of the trees is eight feet. How much does the shorter tree grow in 2 years?
(a)Less than 2 feet
(b)2 feet
(c)$2 \frac{1}{2}$ feet
(d)3 feet
(e)More than 3 feet
Answer
Answer (as printed): A
Explanation
Suppose the taller tree grows $x$ feet in 1 year. Then, the shorter tree grows $\frac{3 x}{5} \mathrm{ft}$ in 1 year. $$\begin{aligned} \therefore \quad 4 x+4 \times \frac{3}{5} x=8 & \Leftrightarrow 4 x+\frac{12}{5} x=8 \Leftrightarrow \frac{32}{5} x=8 \\ & \Leftrightarrow x=\frac{8 \times 5}{32}=\frac{5}{4} . \end{aligned}$$ Growth of shorter tree in 2 years $=\left(2 \times \frac{3 x}{5}\right) \mathrm{ft}$ $$=\left(2 \times \frac{3}{5} \times \frac{5}{4}\right) \mathrm{ft}=\frac{3}{2} \mathrm{ft}=1 \frac{1}{2} \mathrm{ft} .$$
Explanation as extracted from the printed page; notation may be imperfect.