Question

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?

Answer 1

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