Eros went to the grocery store to buy some eggs. He decided to buy both white eggs and brown eggs. He bought 3/5 of a dozen white eggs and 2/3 of a dozen brown eggs. If a dozen contains 12 eggs, what is the ratio of white eggs to brown eggs that Eros bought?
Eros bought 12 x 3/5 = <<12*3/5=7.2>>7.2 white eggs.
Since a dozen contains 12 eggs, then 7.2 is equal to 7 whole eggs and 0.2 x 12 = <<7*0.2*12=16.8>>16.8 eggs.
So Eros bought a total of 7 + 16.8 = <<7+16.8=23.8>>23.8 white eggs.
He bought 12 x 2/3 = <<12*2/3=8>>8 brown eggs.
Therefore, Eros bought 23.8/8 = <<23.8/8=2.975>>2.975 times more white eggs than brown eggs.
Thus, the ratio of white eggs to brown eggs that Eros bought is 2.975:1. Answer: \boxed{2.975:1}.