Answer:
Let's call the number of dimes d and the number of nickels n. We know that d + n = 120, because the combined value of the coins is 120 cents. We also know that n = d + 3, because there are 3 more nickels than dimes.
We can substitute the second equation into the first equation to find the number of dimes and nickels: d + (d + 3) = 120. This simplifies to 2d + 3 = 120, and we can solve for d by subtracting 3 from both sides of the equation: 2d = 117. Dividing both sides by 2, we find that d = 58.5.
Since there are 58.5 dimes and 3 more nickels than dimes, there are 58.5 + 3 = 61.5 nickels. Since we can't have half a coin, we round down to the nearest whole number to find that there are 58 dimes and 61 nickels. Answer: {58, 61}.
If you want 120 candies exactly, the answer is 58.5,61.5.