Jared has a wooden board 11 ft long. He wants to cut it into two pieces so that the longer piece is 4 ft less than 4 times the length of the shorter piece.

Question

How long will each piece of board be?

Enter your answers in the boxes.

Shorter piece:
ft

Longer piece:
ft

Answer 1

Let the length of the shorter piece be \( x \) feet.

According to the problem, the longer piece is 4 ft less than 4 times the length of the shorter piece. Therefore, we can express the length of the longer piece as:

\[ 4x - 4 \]

Since the total length of the board is 11 ft, we can establish the following equation:

\[ x + (4x - 4) = 11 \]

Now, simplify the equation:

\[ x + 4x - 4 = 11 \]

Combine like terms:

\[ 5x - 4 = 11 \]

Add 4 to both sides:

\[ 5x = 15 \]

Now, divide by 5:

\[ x = 3 \]

Thus, the length of the shorter piece is \( 3 \) ft.

Now, we can find the length of the longer piece:

\[ 4x - 4 = 4(3) - 4 = 12 - 4 = 8 \]

Therefore, the lengths of the pieces are:

Shorter piece: 3 ft

Longer piece: 8 ft