Xavior took a total of 124 quarters and dimes to trade in for cash at the bank. He got exactly $25 back. How many quarters did he have?
Let's assume Xavior had q quarters and d dimes.
We know that Xavior took a total of 124 coins, so the equation is q + d = 124. -> equation 1
We also know that the value of quarters (25 cents) times the number of quarters plus the value of dimes (10 cents) times the number of dimes equals $25.
The equation is 25q + 10d = 2500. -> equation 2
To make it easier, we will multiply equation 1 by -10, so it becomes -10q - 10d = -1240.
We will add equation 1 with equation 2, so -10q - 10d + 25q + 10d = -1240 + 2500.
Combining like terms, we get 15q = 1260.
Now, divide both sides of the equation by 15, we get q = 84.
Xavior had 84 quarters. Answer: \boxed{84}.