Large reusable bottles cost $4 more than small ones. Eight large bottles cost $24 less than 12 small ones. How much does one small bottle cost?

First solution can be:

L = S+4

8L = 12S-24 substitute for L:

8 (S+4) = 12S-24

8S+32 = 12S-24 add 24 on both sides and subtract 8S on both sides, and you get:

56 = 4S rewrite to get the unknown on the left:

4S = 56

S = 14 this is the cost of a small bottle.

Other solution can be like this:

Let cost of each small bottle be S

The cost of each large bottle = S + 4

We then get: 8 (S + 4) = 12S - 24

8S - 12S = - 24 - 32

- 4S = - 56

S, or cost of each small bottle = - 56/-4 = $14