Question

a 17 - foot piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. what is the length of the shorter piece? what is the length of the longer piece?

Explanation:

Step1: Let the length of the shorter piece be $x$ feet.

The length of the longer piece is $2x + 5$ feet.

Step2: Set up an equation based on the total length.

The total length of the string is 17 feet, so $x+(2x + 5)=17$.

Step3: Simplify the left - hand side of the equation.

Combining like terms, we get $3x+5 = 17$.

Step4: Solve for $x$.

Subtract 5 from both sides: $3x=17 - 5=12$. Then divide both sides by 3: $x = 4$.

Step5: Find the length of the longer piece.

Substitute $x = 4$ into the expression for the longer piece: $2x+5=2\times4 + 5=8 + 5=13$.

Answer:

The length of the shorter piece is 4 feet and the length of the longer piece is 13 feet.