We were told that the total amount of chips and nuts after doubling is 4 1/2 cups. This contains 1 1/2 cups of peanuts and unknown cups of nuts,c. thus
1 1/2 + c = 4 1/2
c = 4 1/2 - 1 1/2 = 3
Thus, if the original amount of nut is x, then the equation for the original amount of nuts in the recipe is
2x = 3
x = 3/2
x = 1 1/2