Question

a 16-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is two inches more than four times the length of the first piece. find the lengths of the pieces. what is the length of the first piece? what is the length of the second piece? what is the length of the third piece?

Explanation:

Step1: Define variables and equation

Let the length of the first piece be \( x \). The second piece is \( 2x \), and the third is \( 2 + 4x \). The total length is 16, so:

$$ x + 2x + (2 + 4x) = 16 $$

Step2: Simplify the equation

Combine like terms:

$$ 7x + 2 = 16 $$

Step3: Solve for \( x \)

Subtract 2 from both sides:

$$ 7x = 14 $$

Divide by 7:

$$ x = 2 $$

Step4: Find other lengths

Second piece: \( 2x = 2(2) = 4 \)
Third piece: \( 2 + 4x = 2 + 4(2) = 10 \)

Answer:

Length of first piece: \( 2 \) inches
Length of second piece: \( 4 \) inches
Length of third piece: \( 10 \) inches