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?
A.
40
B.
62
C.
84
D.
100
Let's assume that Xavior had q quarters and d dimes.
The total number of coins he had is given by the equation q + d = 124.
The total value of the coins in dollars is given by the equation 0.25q + 0.10d = 25.
We can multiply the second equation by 100 to eliminate the decimals:
25q + 10d = 2500.
Now we can solve the system of equations:
q + d = 124 (equation 1)
25q + 10d = 2500 (equation 2)
From equation 1, we can solve for d: d = 124 - q.
Now, substitute this value of d into equation 2:
25q + 10(124 - q) = 2500
25q + 1240 - 10q = 2500
15q + 1240 = 2500
15q = 1260
q = 84
Therefore, Xavior had 84 quarters.
The correct answer is C. 84.