birds and cages

Question

We have a number of birds and we bought cages to put them in. If we put $7$ birds in each cage then one bird is left over. If we put $9$ birds in each cage then one cage is left over. Find the number of birds and cages.

Any ideas or hints?

Answer 1

If $B$ is the number of birds, and $C$ is the number of cages, we have the following: $$9(C-1) = B\ ;\ \ 7C + 1 = B$$ You can quickly reduce this to find that $\dots$