Final answer:
To find the number of nickels and quarters Jim has, we can set up a system of equations. Solving the system of equations gives us 10 nickels and 14 quarters.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's assume Jim has x number of nickels and y number of quarters. Since he has a total of 24 coins, we know that x + y = 24. Additionally, the value of the coins is $4, so the value of the nickels (which are worth 5 cents each) plus the value of the quarters (which are worth 25 cents each) must equal $4 when converted to cents. This can be expressed as 5x + 25y = 400. Now we can solve this system of equations to find the values of x and y.
We can start by multiplying the first equation by 5 to eliminate x: 5(x + y) = 5(24) → 5x + 5y = 120. Next, we can subtract the new first equation from the second equation to eliminate x: (5x + 25y) - (5x + 5y) = 400 - 120 → 20y = 280. Dividing both sides of the equation by 20 gives us y = 14.
Now, we can substitute the value of y into the first equation to find x: x + 14 = 24 → x = 10. Therefore, Jim has 10 nickels and 14 quarters.