Question

Jack has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have?

Answer 1

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

Answer 2

Let q represent the number of quarters Jack has. Then his collection value is ...
25q +5(50 -q) = 1030
20q = 780
q = 780/20 = 39

Jack has 39 quarters and 11 nickels.