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Jaime has $12.25 in coins. She has only quarters and nickels. If Jaime has exactly 69 coins, how many nickels does she have?

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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.

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