Let the mass of a nut be represented by "x" and the mass of a bolt be represented by "y".
From the given information, we can create the following two equations:
3x + 6y = 72 (Equation 1)
4x + 5y = 66 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the elimination method:
Multiply Equation 1 by 4 and Equation 2 by 3 to eliminate the "x" term:
12x + 24y = 288 (Equation 3)
12x + 15y = 198 (Equation 4)
Subtract Equation 4 from Equation 3:
(12x - 12x) + (24y - 15y) = 288 - 198
9y = 90
y = 10
Substitute the value of "y" into Equation 1 or Equation 2 to find the value of "x".
Using Equation 1:
3x + 6(10) = 72
3x + 60 = 72
3x = 72 - 60
3x = 12
x = 4
Therefore, the mass of a nut is 4g and the mass of a bolt is 10g.