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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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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

#1
+19062
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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?

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

heureka  Dec 2, 2014
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#1
+19062
+8
$$\begin{array}{lrcrcl} (1)& \quad \small{\text{ rabbits } & +& \small{\text{ birds }} &= & 35 \\\\ \hline \\ & \quad 4* \small{\text{ rabbits } &+& 2* \small{\text{ birds }} &=& 94 \quad | \quad :2\\\\ (2) & \quad 2* \small{\text{ rabbits } &+& \small{\text{ birds }} &=& 47 \\\\ \hline \\ (2)-(1): &2* \small{\text{ rabbits }-\small{\text{ rabbits } &+& \small{\text{ birds }} -\small{\text{ birds }} &=& 47-35\\\\ &\small{\text{ rabbits } } &+& 0 &=&12 \\\\ &\small{\text{ rabbits } }&& &=&12 \end{array}\\ \boxed{\small{\text{ rabbits } } =12 } \\ \begin{array}{lrcrcl} (1) & \small{\text{ rabbits } }&+& \small{\text{ birds }} &=& 35 \\ & 12 & + & \small{\text{ birds }} & = & 35 \qquad | \quad -12 \\ & & & \small{\text{ birds }} & = & 35-12 \\ & && \small{\text{ birds }} & = & 23 \end{array} \\ \boxed{birds = 23}$$