Expert: Richard J. Raridon - 9/11/2008

Question
The Holiday Hotel has bedbugs. A single bed has 7 bedbugs  and a double bed has 13 bedbugs. If there are 106 bed bugs in all, how many are double beds.

So, 7x + 13y = 106.
Then what?

Answer
This is known as an indeterminate equation since there more unknowns than equations.  However, you can solve it since x and y have to be integers.  Write it x = (106-13y)/7.  Then start with y = 1,2... until you find a value such that 106-13y is divisible by 7.  In this case, y = 6