When Julia dumped out the big jar of dimes and nickles she found 287 coins. If there was $20.50 in the jar, how many of each kind of coin was there??

d + n = 287

10 d + 5 n = 2050

To find the number of dimes and nickels in the jar, you can set up a system of equations based on the given information.

Let's assume that the number of dimes in the jar is "D" and the number of nickels is "N".

From the given information, we know:

1) The total number of coins is 287, so we can write the equation: D + N = 287.

2) The value of the dimes and nickels combined is $20.50. A dime is worth 10 cents and a nickel is worth 5 cents, so we can write the equation: 10D + 5N = 2050 (since $20.50 is equal to 2050 cents).

Now, we have a system of equations:

Equation 1: D + N = 287
Equation 2: 10D + 5N = 2050

To solve this system of equations, there are various methods you can use, such as substitution or elimination. Let's use the substitution method to find the values of D and N.

From Equation 1, we can rewrite it as D = 287 - N.

Now, substitute this value of D into Equation 2:

10(287 - N) + 5N = 2050
2870 - 10N + 5N = 2050
2870 - 5N = 2050
-5N = 2050 - 2870
-5N = -820
N = -820 / -5
N = 164

So, there were 164 nickels in the jar.

Now, substitute the value of N back into Equation 1:

D + 164 = 287
D = 287 - 164
D = 123

So, there were 123 dimes in the jar.

Therefore, there were 123 dimes and 164 nickels in the jar.