Answer:
Let's use the following variables to represent the number of quarters and nickels:
q = number of quarters
n = number of nickels
We know that the total number of coins is 65, so we can write an equation:
q + n = 65
We also know that the total value of the coins is $6.65, or 665 cents. Since a quarter is worth 25 cents and a nickel is worth 5 cents, we can write another equation:
25q + 5n = 665
Now we have two equations with two variables, which we can solve simultaneously. One way to do this is to solve for one variable in terms of the other in one equation, and then substitute that expression into the other equation. Let's solve the first equation for q:
q + n = 65
q = 65 - n
Now we can substitute that expression for q into the second equation:
25q + 5n = 665
25(65 - n) + 5n = 665
1625 - 20n = 665
-20n = -960
n = 48
So there are 48 nickels in the jar. We can use the first equation to find the number of quarters:
q + n = 65
q + 48 = 65
q = 17
Therefore, there are 17 quarters and 48 nickels in the jar.