Pat throws her loose change into a can on her desk. When she took it out, there were only quarters and nickels. There were a total of 65 coins. If she had a total of $13.65, find the number of quarters and nickels.
To solve this problem, we can set up a system of equations. Let's represent the number of quarters as 'q' and the number of nickels as 'n'.
We know that the total number of coins is 65, so we can write the equation:
q + n = 65
We also know that the total value of the coins is $13.65. Since a quarter is worth $0.25 and a nickel is worth $0.05, we can write the equation:
0.25q + 0.05n = 13.65
Now, we can solve this system of equations to find the values of 'q' and 'n'.
To eliminate decimals, we can multiply both sides of the second equation by 100 to get:
25q + 5n = 1365
Now, we can use the method of substitution or elimination to solve the system of equations.
Let's solve it using the elimination method:
Multiply the first equation by 5 to make the coefficients of 'n' equal and subtract the second equation to eliminate 'n'.
5(q + n) = 5(65)
25q + 5n = 325
Subtract the second equation from the modified second equation:
(25q + 5n) - (25q + 5n) = 325 - 1365
0 = -1040
There is no solution to this system of equations. However, it seems there might be an error in the given information or a mistake in the question itself. Please double-check the information and try again.