I can't figure out how to set it up...

Question

On each 4 legged chair and 3 legged stool, there is a 2 legged person. There is a total of 39 legs. How many chairs and stools are there?

Answer 1

Let x be the number of 4 legged chairs, and y be the number of 3 legged stools.  Since a 2 legged person either sits on a chair or a stool, the number of persons is x + y.

So the total number of legs is 4x + 3y + 2(x+y) or

6x + 5y = 39

 

Since there is 1 equation with 2 unknowns and the solutions must be integers, you just have to list some multiples of 6 and multiples of 5 to see which pair add up to 39.

 

There are 4 chairs and 3 stools.