I have 45 coins in my pocket. They are all either nickels or quarters. Thevalue of the coins is $5.65. How many of each coin do I have?

Sure, let's solve this problem step by step.

Step 1: Let's denote the number of nickels as N and the number of quarters as Q. We know from the problem that N + Q = 45.

Step 2: We also know that the total value of the coins is $5.65. Since a nickel is worth$0.05 and a quarter is worth $0.25, we can write another equation: 0.05N + 0.25Q = 5.65.

Step 3: Now we have a system of two equations, and we can solve it. Let's multiply the first equation by 0.05 to make the coefficients of N the same in both equations: 0.05N + 0.05Q = 2.25.

Step 4: Now, let's subtract this new equation from the second one: 0.05N + 0.25Q - (0.05N + 0.05Q) = 5.65 - 2.25. This simplifies to 0.20Q = 3.40.

Step 5: Solving for Q, we find that Q = 3.40 / 0.20 = 17. So, there are 17 quarters.

Step 6: Substituting Q = 17 into the first equation, we find that N + 17 = 45, which simplifies to N = 45 - 17 = 28. So, there are 28 nickels.

So, you have 28 nickels and 17 quarters.