Question

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?

Answer 1

Hint: Each animal as one head. One buffalo will have 4 legs and one duck will have 2 legs. Form the equation with number of heads & number of legs and then solve to find the number of buffaloes and ducks.

Complete step-by-step answer:
In the question, we have to find the number of buffaloes in the group.
Now let the number of buffaloes be x and the number of ducks are y.
So, the total number of heads in the group of buffaloes and ducks will be \[(x+y)\].
Now, since one buffalo will have 4 legs and one duck will have 2 legs.
So, x buffaloes will have \[4x\] legs and y ducks will have \[2y\]legs.
So here the total legs are \[(4x+2y)\].
Now, it is given that the total number of legs are 24 more than twice the number of heads, so in the equation form it will be:
\[\Rightarrow (4x+2y)=24+2(x+y)\]
Next we will solve for x, to get the number of buffaloes. This is done as follows:
\[\begin{align}
  & \Rightarrow (4x+2y)=24+2(x+y) \\
 & \Rightarrow 4x+2y=24+2x+2y \\
 & \Rightarrow 4x+2y-2y-2x=24 \\
 & \Rightarrow 2x=24 \\
 & \Rightarrow x=12 \\
\end{align}\]
So, here we get the number of buffaloes in the group as 12.

Note: The mistake can happen while simplification and solving the equation. Then expression within the brackets is expanded using the distributive law. Example, \[2(x+y)=2x+2y\].