3x+ 1=z

5y+2=z

Simplified to 3x=5y+ 1.

Because x and y represent degrees, they are integers.

So x=7, y=4 and z=22.

Or x= 12, y=7 and z=37.

Or x= 17, y= 10 and z=52.

Because grandma sent a basket full of eggs.

So x= 17, y= 10 and z=52.

There are 52 eggs.