Answer: there are 118 dimes in the jar.
Step-by-step explanation: Let's use a system of equations to solve the problem:
Let d be the number of dimes and n be the number of nickels.
We know that:
d + n = 250 (Equation 1) (The total number of coins is 250)
0.1d + 0.05n = 18.4 (Equation 2) (The total value of all coins is $18.4)
To solve for d, we need to eliminate n from the equations above. We can do this by multiplying Equation 1 by -0.05 and adding it to Equation 2:
-0.05d - 0.05n = -12.5
0.1d + 0.05n = 18.4
0.05d = 5.9
Dividing both sides by 0.05, we get:
d = 118
Therefore, there are 118 dimes in the jar.