First create a system of equations:
50 = n + q
10.3 = 0.05n + 0.25q
Now pick a method to solve the system of equations. In this case, I'll use the elimination method.
(50 = n + q) x (-0.05)
-2.5 = -0.05n - 0.05q
Now, according to the steps of the elimination method, you add the two equations:
10.3 = 0.05n + 0.25q
- 2.5 = -0.05n - 0.05q
____________________
7.8 = 0n + 0.20q
7.8 = 0.20q
Now, solve for the remaining variable:
(7.8)/0.20 = (0.20q)/0.20
39 = q
Therefore, there are 39 quarters. 39 quarters equals $9.75, so you can use this value to calculate the number of nickels by subtracting this amount from the total amount, and then dividing the left overs by the value of the nickel.
$10.30 - $9.75 = $0.55
$0.55 / $0.05 = 11
So there are 11 nickels and 39 quarters. To confirm the answer, make sure the number of coins adds up to 50.
11 + 39 = 50
