Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A 12-ft. board is cut into 2 pieces so that one piece is 4 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
A) shorter piece: 6 ft; longer piece: 36 ft
B) shorter piece: 2 ft; longer piece: 10 ft
C) shorter piece: 12 ft; longer piece: 40 ft
D) shorter piece: 32 ft; longer piece: 36 ft

Question

Quizplus · Accepted Answer

Let the length of the shorter piece be x. Then the length of the longer piece is 3x+4. The sum of the lengths of the two pieces is equal to the length of the original board, which is 12 feet. 
So, we can write the equation: 
x + (3x+4) = 12 
Simplifying and solving for x, we get: 
4x + 4 = 12 
4x = 8 
x = 2 
Therefore, the length of the shorter piece is 2 feet and the length of the longer piece is 3x+4 = 10 feet. 
So, the answer is B. Let x be the length of the shorter piece.
Then the longer piece is 3x+4.
The sum of the two pieces is 12 feet.
So, x + (3x+4) = 12.
Solving for x, we get x=2.
Therefore, the lengths of the two pieces are 2 feet and 10 feet. This matches choice B.

Set Up an Equation That Can Be Used to Solve