Question

Joe’s chair shop makes 3 legged stools and 4 legged stools. At the end of one day they looked at the materials that they used. They used 63 legs and they produced 19 total stools. How many of the stools were 3 legged and how many were 4 legged?

Answer 1

Let x represent number of 3 legged stools and y represent number of 4 legged stools.  

We have been given that at the end of one day Joe's chair shop produced 19 total stools. We can represent this information in an equation as:

$x+y=19...(1)$

$y=19-x...(1)$

We are also told that Joe's chair shop used 63 legs. We can represent this information in an equation as:

$3x+4y=63...(1)$

Upon substituting equation (1) in equation (2), we will get:

$3x+4(19-x)=63$

$3x+76-4x=63$

$-x+76=63$

$-x+76-76=63-76$

$-x=-13$

$\frac{-x}{-1}=\frac{-13}{-1}$

$x=13$

Therefore, 13 stools were 3 legged.

Upon substituting $x=13$ in equation (1), we will get:

$y=19-13=6$

Therefore, 6 stools were 4 legged.