Xavier took a total of 124 quarters and dimes to trade in for cash at the bank he got exactly 25 dollars back how many quarters did he have?
Let x be the number of quarters.
The number of dimes is 124 - x.
The total value of quarters is 0.25x.
The total value of dimes is 0.1(124 - x).
The total value of all coins is 0.25x + 0.1(124 - x) = 25.
0.25x + 12.4 - 0.1x = 25
0.15x + 12.4 = 25
0.15x = 12.6
x = <<84=84>>84
Xavier had 84 quarters. Answer: \boxed{84}.