In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
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Let’s denote the number of buffaloes as \(b\) and the number of ducks as \(d\).
Since each buffalo has 4 legs and each duck has 2 legs, the total number of legs in the group is \(4b + 2d\). The total number of heads, which is also the total number of animals, is \(b + d\).
According to the problem, the number of legs is 24 more than twice the number of heads. Therefore, we can write the equation:
\[4b + 2d = 2(b + d) + 24\]
Simplifying this equation:
\[4b + 2d = 2b + 2d + 24\]
\[2b = 24\]
\[b = 12\]
So, there are 12 buffaloes in the group.