Final answer:
Xavior had 84 quarters. Using two equations, one for the total number of coins and another for their total value, the number of quarters (q) and dimes (d) can be found. By solving the equations, we find q equals 84.
Step-by-step explanation:
To solve the problem, we need to set up two equations using the given information. Let's denote the number of quarters as q and the number of dimes as d. We're given that Xavior has a total of 124 coins, so our first equation is:
q + d = 124
We also know that Xavior got $25 back for these coins. Since a quarter is worth $0.25 and a dime is $0.10, our second equation based on the value of the coins is:
0.25q + 0.10d = 25
To solve these equations simultaneously, we'll first multiply the second equation by 10 to eliminate the decimals:
2.5q + d = 250
Next, we subtract the first equation from this new equation:
1.5q = 250 - 124
1.5q = 126
Now, we divide by 1.5 to find the number of quarters:
q = 126 / 1.5
q = 84
So, Xavior had 84 quarters.