Answer:
40 nickels
45 dimes
15 quarters
Explanation:
Let's use the following variables to represent the number of each type of coin:
N = number of nickels
D = number of dimes
Q = number of quarters
We know that:
- N + D + Q = 100 (because there are a total of 100 coins)
- 0.05N + 0.10D + 0.25Q = 10.25 (because the total value of the coins is $10.25)
- D = 3Q (because there are three times as many dimes as quarters)
Now we can substitute the third equation into the first two equations to get:
N + 4Q = 100 (equation 1, obtained by substituting D = 3Q)
5N + 10D + 25Q = 1025 (equation 2, obtained by substituting D = 3Q and simplifying)
We can simplify equation 1 by multiplying both sides by 5:
5N + 20Q = 500
Now we can subtract this equation from equation 2 to eliminate N:
10D + 5Q = 525
Next, we can substitute D = 3Q into this equation to get:
10(3Q) + 5Q = 525
Simplifying:
35Q = 525Q = 15
So there are 15 quarters.
We can use D = 3Q to find that there are 45 dimes.
Finally, we can use N + 4Q = 100 to find that there are 40 nickels.
Therefore, there are 40 nickels, 45 dimes, and 15 quarters.