Alice, Bob, Cathy and Dan went to Easter egg hunt.
They found red, orange, yellow and green colored eggs.
Solution:
Let T be the total number of eggs they found.
Let R, O, Y and G be the number of red, orange, yellow and
green eggs respectively.
Among the eggs they found, the number of red eggs were
twice the number of green eggs. The yellow eggs were two more than the red
eggs. The orange eggs were three more than the green eggs.
Therefore,
R = 2G, Y=2G+2, O=G+3
G + R + Y + O = (G) + (2G) + (2G+2) + (G+3) = T
6G+5 = T (*1)
Let A, B, C, and D be the number of eggs Alice, Bob, Cathy
and Dan found respectively.
Alice found as many eggs as Bob did. Cathy found
three eggs more than Alice did. Dan found four eggs more than Bob did.
Therefore
A = B, C = A+3, D = B+4
A + B + C + D = (A) + (A) + (A+3) + (A+4) = T
4A + 7 = T (*2)
Cathy, whose favorite color is red gathered only red
colored eggs. None of the other kids gathered red colored eggs.
C = R
A + 3 = 2G (*3)
From (*1) and (*2)
6G + 5 = 4A + 7 (*4)
Solving (*3) and (*4) simultaneouly, we have
A = 7, G = 5
By further substitution, we have
5 green, 10 red, 8 orange and 12 yellow eggs for a total of
35 eggs. Alice, Bob, Cathy and Dan found 7, 7, 10 and 11 eggs
respectively.
