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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?

User Nwly
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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.

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User Joe McGrath
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