Final answer:
To find out how many nickels and quarters Sally has, we can set up a system of equations using the given information. By solving the system of equations, we find that Sally has 6 nickels and 9 quarters.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's represent the number of nickels as 'x' and the number of quarters as 'y'. We know that there are a total of 15 coins, so x + y = 15. We also know that the total value of the coins is $2.55, which can be represented as 0.05x + 0.25y = 2.55.
To solve this system of equations, we can use the method of substitution or elimination. I'll use the substitution method. From the first equation, we can solve for x in terms of y: x = 15 - y. Substituting this into the second equation:
0.05(15 - y) + 0.25y = 2.55
0.75 - 0.05y + 0.25y = 2.55
0.20y = 1.80
y = 1.80/0.20 = 9
Substituting this value of y back into the first equation:
x + 9 = 15
x = 15 - 9 = 6
So, Sally has 6 nickels and 9 quarters.