20cm cake serves 12 people costs 13.50 per cake and 25cm cake serves 20 people costs 18.75 . there will be 57 guests and want to make sure everyone gets a slice . want to pay as little for the cakes and want the cakes to be the same size 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.