Two women shared 5 dozen eggs in the ratio 1:2. how many eggs does each receive?

If the ratio is 1:2 means that one is the double of the other, then if they shared 5 dozen, that is 5*12 = 60 total eggs, so we need two numbers that add to 60 and one is the double of the other, that is two equations just said, let the numbers by x, y:

x + y = 60

y = 2x

substitute:

x + 2x = 60

x = 20

substitute:

y = 2x = 2*20

y = 40

those are the numbers, they receive 20 and 40