Question

carpentry a carpenter has a piece of wood that is 78 inches long. he wants to cut it so that one piece is five times as long as the other piece. what are the lengths of the two pieces?
a) 12 in. and 60 in.
b) 13 in. and 65 in.
c) 13 in. and 52 in.
d) 11 in. and 67 in.

Explanation:

Step1: Define variables

Let the shorter piece be \( x \) inches, then the longer piece is \( 5x \) inches.

Step2: Set up equation

The total length is 78 inches, so \( x + 5x = 78 \).

Step3: Solve equation

Combine like terms: \( 6x = 78 \). Divide both sides by 6: \( x = \frac{78}{6} = 13 \).

Step4: Find longer piece

Longer piece: \( 5x = 5\times13 = 65 \).

Answer:

B) 13 in. and 65 in.