Xavier took a total of 124 quarters and dimes to trade in for cash at the bank. He got exactly 25 backs how many quarters did he have
Let q be the number of quarters and d be the number of dimes.
According to the given information, we have two equations:
q + d = 124 (total number of coins)
0.25q + 0.10d = 25 (total value of coins in dollars)
To solve for q, we can first rewrite the second equation as:
25 = 0.25q + 0.10(124 - q)
25 = 0.25q + 12.40 - 0.10q
25 = 0.15q + 12.40
12.60 = 0.15q
q = 84
Therefore, Xavier had 84 quarters.