Let's assume the weight of a chicken egg is represented by 'c' and the weight of a duck egg is represented by 'd'.
From the given information, we can form two equations:
Equation 1: 3c + 5d = 500 (Total weight of three chicken eggs and five duck eggs is 500 g)
Equation 2: 7c + 5d = 700 (Total weight of seven chicken eggs and five duck eggs is 700 g)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of elimination to eliminate 'd' from the equations:
Multiply Equation 1 by 7: 21c + 35d = 3500
Multiply Equation 2 by 3: 21c + 15d = 2100
Subtract Equation 2 from Equation 1:
(21c + 35d) - (21c + 15d) = 3500 - 2100
20d = 1400
d = 70
Now, substitute the value of 'd' back into Equation 1 or Equation 2 to find the value of 'c':
3c + 5d = 500
3c + 5(70) = 500
3c + 350 = 500
3c = 150
c = 50
Therefore, each chicken egg weighs 50 grams and each duck egg weighs 70 grams.