Question

a 15-foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. find the lengths of both pieces. what is the length of the shorter piece?

Explanation:

Step1: Define variables

Let the length of the shorter piece be $x$ feet. Then the longer piece is $2x + 3$ feet (since it's 3 feet longer than twice the shorter piece).

Step2: Set up equation

The total length of the string is 15 feet, so the sum of the two pieces is 15. So we have the equation: $x+(2x + 3)=15$.

Step3: Solve the equation

First, combine like terms: $3x+3 = 15$. Then subtract 3 from both sides: $3x=15 - 3=12$. Then divide both sides by 3: $x=\frac{12}{3}=4$.

Answer:

The length of the shorter piece is 4 feet.