Final answer:
Jaime has 25 nickels. This is determined by setting up and solving a system of equations based on the total value of coins and the number of coins.
Step-by-step explanation:
To determine how many nickels Jaime has, we can set up a system of equations based on the total value of the coins and the total number of coins.
Let N represent the number of nickels and Q represent the number of quarters. We know that each nickel is worth $0.05 and each quarter is worth $0.25. Jaime has $12.25 in total, and she has 69 coins.
The two equations representing the situation are:
0.05N + 0.25Q = 12.25 (Total value of coins)
N + Q = 69 (Total number of coins)
Multiplying the second equation by 0.05 gives us:
0.05N + 0.05Q = 3.45
Subtracting this new equation from the first equation, we get:
0.25Q - 0.05Q = 12.25 - 3.45
0.20Q = 8.80
Dividing both sides by 0.20 gives us:
Q = 44
Now, using the second equation (N + Q = 69), we substitute 44 for Q:
N + 44 = 69
N = 69 - 44
N = 25
So, Jaime has 25 nickels.