Final answer:
To solve the problem, we set up a system of equations based on the number of coins and their total value. We find that Sarah has 11 nickels and 6 quarters, which corresponds to option c.
Step-by-step explanation:
We are asked to determine the number of quarters and nickels Sarah has if she has a total of 39 coins consisting of nickels, dimes, and quarters worth $4.25, with twice as many dimes as nickels. Let's denote the number of nickels as N, the number of dimes as D, and the number of quarters as Q. Since Sarah has twice as many dimes as nickels, we can write D = 2N. The total number of coins is given by N + D + Q = 39. In terms of the total value, nickels are worth 5 cents, dimes 10 cents, and quarters 25 cents, so the value equation is 5N + 10D + 25Q = 425 cents (since $4.25 is 425 cents).
Substituting D = 2N into our equations, we get N + 2N + Q = 39 and 5N + 10(2N) + 25Q = 425. Simplifying, we get 3N + Q = 39 and 25N + 25Q = 425. Dividing the second equation by 25, we get N + Q = 17. Now we have a system of two equations with two variables:
Subtract the second equation from the first, yielding 2N = 22. Dividing by 2, we find N = 11. Plugging N = 11 into N + Q = 17, we find Q = 6. Sarah has 11 nickels and 6 quarters, which means the correct answer is option c: 11 nickels and 6 quarters.