Final answer:
The initial setup for the equation based on the coin values and the total amount led to an incorrect result with a negative number of nickels. This suggests there was an error in the calculations or assumptions, and the equation should be revisited and the numbers checked to find the correct number of each type of coin.
Step-by-step explanation:
Let's call the number of nickels Sarah has n. According to the problem, Sarah has 10 more dimes than nickels, which means she has n+10 dimes. It is also given that she has twice as many quarters as dimes, making it 2(n+10) quarters. In terms of their values, nickels are worth 5 cents, dimes are worth 10 cents, and quarters are worth 25 cents. The total value of Sarah’s coins is $9.25, which is equivalent to 925 cents.
To find the number of each coin, we can set up the following equation:
5n + 10(n+10) + 25(2(n+10)) = 925
Simplifying the equation:
5n + 10n + 100 + 50n + 1000 = 925
65n + 1100 = 925
65n = 925 – 1100
65n = -175
n = -175 / 65
n = -2.6923
This result is not possible since we cannot have a negative number of coins. It seems there was an error in the calculations or assumptions. It is important to check the equation and numbers we're using to ensure they properly represent the coin values and the total amount.