Question

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.

Answer 1

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

`\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=(72)/(6)in=12in \end{gathered}`

Therefore the longest piece is

`L=4M=4\cdot(12)=48in`