There are 57 people and i want everyone to have a slice of cake and i want to pay as little as possible and I want them to be the same size so I have 20cm of cake that can serve12 people costs 13.50 per cake or 25 cm of cake that I can serve to 20 people costs 18.75 per cake How much will I have to pay for the cakes

So,

If you do some simple division, you will find how much each cm costs in each cake.

20cm cake = 67.5 cents/cm

25cm cake = 93.75 cents/cm

Assuming that you cannot order fractions of cakes, the best deal would be to order 5 of the 20cm cakes.

Cost = 13.50 * 5 = $67.50

You will have to pay $67.50 for the cakes if you want the best deal.