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Solution to Puzzle 153 EASTER EGGS

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.

 

 

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