answer:
To solve the problem, we can use a system of equations to represent the given information. Let's denote the number of dimes as "d" and the number of quarters as "q".
From the problem, we have two pieces of information:
1. The total value of the coins is $7.65. We can express this as an equation: 0.10d + 0.25q = 7.65.
2. The total number of coins is 45. We can express this as another equation: d + q = 45.
Now, we can solve this system of equations to find the values of d and q.
One way to do this is by substitution. We can solve the second equation for d and substitute it into the first equation:
d = 45 - q
0.10(45 - q) + 0.25q = 7.65
4.50 - 0.10q + 0.25q = 7.65
0.15q = 7.65 - 4.50
0.15q = 3.15
q = 3.15 / 0.15
q ≈ 21
Substitute the value of q back into the second equation to find d:
d + 21 = 45
d = 45 - 21
d = 24
Therefore, Allan has 24 dimes and 21 quarters.
The correct answer is option D) 24 dimes, 21 quarters.
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