Question

I don't understand how to do this equation. The string is 108 inches. The string is cut into 3 pieces. One piece is 2 inches longer than the shortest piece., and the longest piece is 4 inches longer than the shortest piece. How long is the longest piece?

Answer 1

Start by sketching the situation, dividing the string into 3 pieces

Call the shortest piece as x

Then since the other pieces are a reference to the shortest side we can call them as:

`\begin{gathered} x+2 \\ x+4 \end{gathered}`

Then, add them to the sketch

If we add together the 3 pieces they must be equal to the initial length of the string

`x+(x+2)+(x+4)=108`

Simplify the left side of the equation

`\begin{gathered} 3x+6=108 \\ \end{gathered}`

Solve the equation for x

`\begin{gathered} 3x+6-6=108-6 \\ 3x=102 \\ x=(102)/(3) \\ x=34 \end{gathered}`

The shortest piece is 34 inches long.

The longest piece is 4 inches longer than the shortest, then,

`34+4=38`

The longest piece is 38 inches long.