Liam is setting up folding chairs for a meeting. If he arranges the chairs in 6 rows of the same length, he has 7 chairs left over. If he arranges the chairs in 4 rows of that same length, he has 13 left over. How many
chairs does Liam have?

We will need to have two equations here, having x as the missing length. We know that the chairs are in the same amount on each occasion, so each equation should be equal to the other.

This sets up a problem of:

6x + 7 = 4x + 13

7 and 13 being the leftover chairs and 6 and 4 being the rows. Let’s solve for x.

x = 3

Knowing this, we plug in x for one of the equations

6(3) + 7
18 + 7
25

Liam has 25 chairs.