Solution to the Problem:
1) There were 10 red eggs.
2) There were 8 purple eggs.
3) There were 12 yellow eggs.
4) There were 5 green eggs.
5) Amy found 7 eggs.
6) Ben found 7 eggs.
7) Carrie found 10 eggs.
8) David found 11 eggs.
Let G = number of green eggs
Let R = number of red eggs
Let P = number of purple eggs
Let Y = number of yellow eggs
Let A = number of eggs that Amy found
Let B = number of eggs that Ben found
Let C = number of eggs that Carrie found
Let D = number of eggs that David found
Then set up the equations:
P = G + 3
R = 2G
Y = R + 2
A = B
C = A + 3
D = B + 4
C = R
A + B + C + D = G + R + P + Y
That gives you eight equations with eight variables.
You can express all the variables in terms of G.
R = 2G
P = G + 3
Y = 2G + 2
C = 2G
A = 2G - 3
B = 2G - 3
D = 2G + 1
Substituting into the 8th equation, we get
8G - 5 = 6G + 5
Then 2G = 10
So G = 5
Then R = 10
P = 8
Y = 12
A = 7
B = 7
C = 10
D = 11.