Coins and Cakes

Miriam has coins of two shekels and of five shekels.

If she pays only with two-shekel coins, she will be 60 shekels short of buying 4 cakes.

If she pays only with five-shekel coins, she will be 60 shekels short of buying 5 cakes.

In total, she is 60 shekels short of buying 6 cakes. How much does a cake cost?