Use an algebraic approach to solve the problem: A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.
A)20 feet
B)4 feet
C)12 feet
D)-4 feet
E)8 feet

Question

Quizplus · Accepted Answer

Let the length of the shorter piece be $x$ feet. Then, the length of the longer piece is $\frac{2}{3}x$ feet. Since the total length of the board is 20 feet, we have $x + \frac{2}{3}x = 20$. Solving for $x$, we find that $x = 8$ feet, making the shorter piece 8 feet long.

Use an Algebraic Approach to Solve the Problem: a Board