Gina sells 216 cakes in the ratio small : medium:large 5:7:12. The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake. Her total profit id £648.45. Work out the profit for one small cake.

Total number of cakes sold 216

ratio of small:medium:large is 5:7:12

The total profit is $648.45

Let the profit made from small cake be x

profit made from medium cake will 2x

profit for large cake is 3x

the total profit will be:

x+2x+3x=648.45

6x=648.45

x=648.45/6

x=108.075

the profit for small size is $108.075

the profit for medium size will be 108.075*2=$216.15

the profit for large size is 108.075*3=$324.225