A drove of sheep and chickens have a total of 99 heads and feet. There are twice as many chickens as sheep. How many of each are there?
Solution: There are 9 sheep and 18 chickens.
Let S be the number of sheep and C be the number of chickens. So:
2S = C
5S + 3C = 99
We can rephrase the first equation, so:
6S – 3C = 0
And then we can add this to the second equation, which yields:
11S = 99
By solving for S, we find that S equals 9. By substituting back in one of the original equations, we find that C equals 18. So there are nine sheep and eighteen chickens.