Final answer:
To find the number of nickels in the jar, we can set up a system of equations using the total number of coins and the total value of the coins. Solving this system, we find that there are 19 nickels in the jar.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let x be the number of nickels and y be the number of dimes. We know there are 40 coins in total, so we have the equation x + y = 40. We also know that the value of the coins is $3.10, which can be represented as 0.05x + 0.1y = 3.10. Solving this system of equations, we can find that there are 19 nickels in the jar. Therefore, the answer is 19.