Answer: Stacy has 10 nickels, 2 pennies, and 7 quarters
Let's use algebra to solve this problem.
N = the number of nickels
P = the number of pennies
Q = the number of quarters
We're given three pieces of information:
Stacy has five times as many nickels as pennies, so we can write the equation:
N = 5P
She has five more quarters than pennies, so we can write the equation:
Q = P + 5
The total value of her change is $2.27, which we can express in cents as 227 cents:
5N (nickels) + P (pennies) + 25Q (quarters) = 227
Now, let's use these equations to solve for N, P, and Q. We'll start by substituting the values from the first two equations into the third equation:
5(5P) + P + 25(P + 5) = 227
Now, simplify and solve for P:
25P + P + 25P + 125 = 227
Combine like terms:
51P + 125 = 227
Subtract 125 from both sides:
51P = 227 - 125
51P = 102
Now, divide by 51 to find the value of P:
P = 102 / 51
P = 2
Now that we know P (pennies), we can find N (nickels) and Q (quarters) using the equations from earlier:
N = 5P
N = 5 * 2
N = 10
Q = P + 5
Q = 2 + 5
Q = 7
So, Stacy has 10 nickels, 2 pennies, and 7 quarters in her pocket.