Total Fraction of Cakes Purchased

A bakery sells three sizes of cakes: small, medium, and large. The size of the cakes and their respective prices are as follows:

Small cake: $\frac{2}{5}$ of a whole cake, priced at $10.
Medium cake: $\frac{3}{5}$ of a whole cake, priced at $15.
Large cake: whole cake, priced at $25.

Each size of cake is made from the same ingredients, but the proportions vary by size. If a customer buys:

• 1 small cake
• 2 medium cakes
• 1 large cake

What fraction of a whole cake does the customer effectively purchase in total?