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There are 35 rabbits and birds combined in one cage. There are 94 legs in the cage. How may rabbits and how many birds are there?

 

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Guest Dec 2, 2014

Best Answer 

 #1
avatar+20680 
+8

There are 35 rabbits and birds combined in one cage. There are 94 legs in the cage. How may rabbits and how many birds are there?

$$\begin{array}{lrcrcl}
(1)& \quad \small{\text{ rabbits } & +& \small{\text{ birds }} &= & 35 \\\\
\hline \\
& \quad 4* \small{\text{ rabbits } &+& 2* \small{\text{ birds }} &=& 94 \quad | \quad :2\\\\
(2) & \quad 2* \small{\text{ rabbits } &+& \small{\text{ birds }} &=& 47 \\\\
\hline \\
(2)-(1): &2* \small{\text{ rabbits }-\small{\text{ rabbits } &+& \small{\text{ birds }} -\small{\text{ birds }} &=& 47-35\\\\
&\small{\text{ rabbits } } &+& 0 &=&12 \\\\
&\small{\text{ rabbits } }&& &=&12
\end{array}\\
\boxed{\small{\text{ rabbits } } =12 } \\
\begin{array}{lrcrcl}
(1) & \small{\text{ rabbits } }&+& \small{\text{ birds }} &=& 35 \\
& 12 & + & \small{\text{ birds }} & = & 35 \qquad | \quad -12 \\
& & & \small{\text{ birds }} & = & 35-12 \\
& && \small{\text{ birds }} & = & 23
\end{array}
\\
\boxed{birds = 23}$$

heureka  Dec 2, 2014
 #1
avatar+20680 
+8
Best Answer

There are 35 rabbits and birds combined in one cage. There are 94 legs in the cage. How may rabbits and how many birds are there?

$$\begin{array}{lrcrcl}
(1)& \quad \small{\text{ rabbits } & +& \small{\text{ birds }} &= & 35 \\\\
\hline \\
& \quad 4* \small{\text{ rabbits } &+& 2* \small{\text{ birds }} &=& 94 \quad | \quad :2\\\\
(2) & \quad 2* \small{\text{ rabbits } &+& \small{\text{ birds }} &=& 47 \\\\
\hline \\
(2)-(1): &2* \small{\text{ rabbits }-\small{\text{ rabbits } &+& \small{\text{ birds }} -\small{\text{ birds }} &=& 47-35\\\\
&\small{\text{ rabbits } } &+& 0 &=&12 \\\\
&\small{\text{ rabbits } }&& &=&12
\end{array}\\
\boxed{\small{\text{ rabbits } } =12 } \\
\begin{array}{lrcrcl}
(1) & \small{\text{ rabbits } }&+& \small{\text{ birds }} &=& 35 \\
& 12 & + & \small{\text{ birds }} & = & 35 \qquad | \quad -12 \\
& & & \small{\text{ birds }} & = & 35-12 \\
& && \small{\text{ birds }} & = & 23
\end{array}
\\
\boxed{birds = 23}$$

heureka  Dec 2, 2014

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