Final answer:
To find the number of nickels, quarters, and dimes, we can set up a system of equations. From the given information, we assign variables to the unknown quantities and create an equation based on the total value of the coins. Simplifying the equation will give us the system of equations to solve. By solving the equations, we find that there are 3 nickels, 8 quarters, and 18 dimes.
Step-by-step explanation:
To set up a system of equations to find the number of nickels, quarters, and dimes, we need to use the given information to create equations. Let's start by assigning variables to the unknown quantities:
Let x be the number of dimes.
Then, the number of quarters will be x - 10 (10 fewer quarters than dimes).
And the number of nickels will be (x - 10) - 5 (5 fewer nickels than quarters).
We also know the total value of the coins is $4.75. We can use the values of the coins to create the equation:
0.10x + 0.25(x - 10) + 0.05((x - 10) - 5) = 4.75
Simplifying this equation will give us the system of equations we need to solve to find the number of nickels, quarters, and dimes:
0.10x + 0.25x - 2.50 + 0.05x - 0.25 = 4.75
0.40x - 2.75 = 4.75
0.40x = 7.50
x = 18.75
Since we can't have a fractional number of coins, we round down to the nearest whole number:
x ≈ 18
Therefore, you have 18 dimes, 18 - 10 = 8 quarters, and (18 - 10) - 5 = 3 nickels.