mathschallenge.net

Problem

A cage contains birds and rabbits. There are sixteen heads and thirty-eight feet. How many birds are there in the cage?

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Solution

If we let the number of birds be represented by $b$ and the number of rabbits be represented by $r$ then we get the following two equations:

$$\begin{aligned}b + r &= 16     (1)\\2b + 4r & = 38     (2)\end{aligned}$$

Dividing the second equation by two gives:

$$b + 2r = 19     (3)$$

If we now subtract equation $(1)$ from equation $(3)$ we get $r = 3,$ and as $b + r = 16$ it follows that the number of birds, $b = 13$.

What if you were told that the number of feet was equal to twice the number of heads?
What if there were sixteen heads and twenty-eight feet?