Bakery Pastry Sales Problem

A local bakery produces two types of pastries: croissants and danishes. The bakery sells croissants for $3 each and danishes for $4 each. On a busy Saturday morning, the bakery sold a total of 180 pastries, earning a total of $600.

If we let x represent the number of croissants sold and y represent the number of danishes sold, we can form the following system of equations:

$$(x + y = 180)$$

and

$$(3x + 4y = 600)$$

Determine the value of y, the number of danishes sold, as a fraction in simplest form.