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2. Nathaly has a piece of board 67 incheslong. She cuts it into three pieces. Thelongest piece is four times the length of themiddle-sized piece, and the shortest piece is5 inches shorter than the middle-sizedpiece. Find the length of the longest piece.

Respuesta :

Everything depands on the middle piece, so we have to write the length of the board in terms of the middle piece.

[tex]\begin{gathered} 4M\text{ =L} \\ M-5=S \\ L+M+S=67 \\ \therefore\rightarrow \\ 4M+M+(M-5)=67in \\ 4M+M+M=72in\rightarrow6M=72in\rightarrow M=\frac{72}{6}in=12in \end{gathered}[/tex]

Therefore the longest piece is

[tex]L=4M=4\cdot(12)=48in[/tex]

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