To find the number of nickels, dimes, and quarters, let's set up a system of equations.
Let's say the number of nickels is "n", the number of dimes is "d", and the number of quarters is "q".
We are given three pieces of information:
1. The total value of the coins is $8.75. Since a nickel is worth $0.05, a dime is worth $0.10, and a quarter is worth $0.25, we can express the total value as an equation:
0.05n + 0.10d + 0.25q = 8.75.
2. There are 5 more dimes than nickels. We can express this as an equation:
d = n + 5.
3. There are 9 more quarters than nickels. We can express this as an equation:
q = n + 9.
Now, let's solve this system of equations to find the values of n, d, and q.
Substitute the second equation into the first equation:
0.05n + 0.10(n + 5) + 0.25(n + 9) = 8.75.
Simplify and solve for n:
0.05n + 0.10n + 0.50 + 0.25n + 2.25 = 8.75.
0.40n + 2.75 = 8.75.
0.40n = 6.
n = 15.
Now, substitute the value of n back into the second and third equations to find d and q:
d = 15 + 5 = 20.
q = 15 + 9 = 24.
Therefore, she has 15 nickels, 20 dimes, and 24 quarters.