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A rope 580 cm long is to be cut into 40 cm and 90 cm segments without any wastage. How many ways are there to do this?
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\begin{equation}40x+90y=580 \end{equation} The following values satisfy \begin{aligned} x&= 10, \ y=2 \\ x&=1, \ \ y=6 \end{aligned} Thus, 2 ways.
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A piece of land 400 meters long is to be cut into 40 meter and 60 meter segments without any wastage. How many ways are there to do this?
\begin{equation*}40x+60y=400 \end{equation*} The following values satisfy \begin{align*} x=1 \\ y=6 \\ \\ x=4 \\ y=4 \\ \\ x=7 \\ y=2 \\ \\ \end{align*}Thus, 3 ways.
A roll of wall paper 400 cm long is to be cut into 40 cm and 60 cm segments without any wastage. How many ways are there to do this?
A rope 410 cm long is to be cut into 40 cm and 60 cm segments without any wastage. How many ways are there to do this?
\begin{equation*}40x+60y=410 \end{equation*} The following values satisfy \begin{align*} \end{align*}Thus, 0 ways.
A piece of cloth is 410 cm long is to be cut into 40 cm and 60 cm lengths without any wastage. How many ways are there to do this?
A piece of land 410 meters long is to be cut into 40 meter and 60 meter segments without any wastage. How many ways are there to do this?
A roll of wall paper 410 cm long is to be cut into 40 cm and 60 cm segments without any wastage. How many ways are there to do this?
A rope 420 cm long is to be cut into 40 cm and 60 cm segments without any wastage. How many ways are there to do this?
\begin{equation*}40x+60y=420 \end{equation*} The following values satisfy \begin{align*} x=3 \\ \\ y=5 \\ \\ x=6 \\ \\ y=3 \\ \\ x=9 \\ \\ y=1 \\ \\ \end{align*}Thus, 3 ways.
A piece of cloth is 420 cm long is to be cut into 40 cm and 60 cm lengths without any wastage. How many ways are there to do this?
\begin{equation*}40x+60y=420 \end{equation*} The following values satisfy \begin{align*} x=3 \\ \\ y=5 \\ \\ x=6 \\ \\y=3 \\ \\ x=9 \\ \\ y=1 \\ \\ \end{align*}Thus, 3 ways.
A piece of land 420 meters long is to be cut into 40 meter and 60 meter segments without any wastage. How many ways are there to do this?
\begin{equation*}40x+60y=420 \end{equation*} The following values satisfy \begin{align*} x&=3, \\ y=5.0 \\ x&=6, \\ y=3.0 \\ x&=9, \\ y=1.0 \\ \end{align*}Thus, 3 ways.
A roll of wall paper 420 cm long is to be cut into 40 cm and 60 cm segments without any wastage. How many ways are there to do this?
\begin{equation*}40x+60y=420 \end{equation*} The following values satisfy \begin{align*} x=3 \\ \\ y=5 \\ \\ x=6, \\ \\ y=3 \\ \\ x=9 \\ \\ y=1 \\ \end{align*}Thus, 3 ways.
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