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 q be the number of quarters and d be the number of dimes. We know that q + d = 124 and 0.25q + 0.1d = 25.
We can multiply both sides of the first equation by 0.1 to get 0.1q + 0.1d = 12.4
We can subtract the equation above by the second equation to get 0.15q = 12.4
Dividing both sides by 0.15 gives q = 82. Answer: \boxed{82}.
are you sure?
Apologies for the mistake in my previous response.
Let's correct the solution:
Let q be the number of quarters and d be the number of dimes. We have two equations:
q + d = 124 ..........(1)
0.25q + 0.10d = 25 .........(2)
Multiplying equation (2) by 100 to remove decimals:
25q + 10d = 2500 ........(3)
Multiplying equation (1) by 10:
10q + 10d = 1240 ........(4)
Now, subtracting equation (4) from equation (3):
(25q + 10d) - (10q + 10d) = 2500 - 1240
15q = 1260
q = 1260/15
q = 84
Xavior had 84 quarters.