Problem Solving

Manhattan Prep

Two trees have a combined height of 60 feet, and the taller tree is \(x\) times the height of the shorter tree. How tall is the shorter tree, in term of \(x\)?

A. \(\frac{60}{1+x}\)
B. \(\frac{60}{x}\)
C. \(\frac{30}{x}\)
D. \(60-2x\)
E. \(30-5x\)

OA A

Let the taller tree = T
Let the shorter tree = S
$$T+S=60ft---eqni$$
$$T=x\cdot S---equ\ ii$$
$$substituting\ \left(X\cdot S\right)for\ T\ in\ equ\ i$$
$$\left(x\cdot S\right)+S=60$$
$$xS+S=60$$
$$S\left(x+1\right)=60$$
divide through by coefficient of S
$$\frac{S\left(x+1\right)}{x+1}=\frac{60}{x+1}$$
$$S=\frac{60}{x+1}$$

$$Answer\ is\ Option\ A$$