Question

I have 30 coins consisting of nickels and quarters. The total value of the coins is $4.10. How many of each kind do I have?

Answer 1

n + q = 30
n(0.05) + q(0.25) = 4.10
17(0.05) + 13(0.25)
17 + 13 = 30
0.85 + 3.25 = 4.10
You have 17 nickels and 13 quarters.

Answer 2

17 nickels and 13 quarters.

Explanation:

1 Nickel = 0.05 dollar

1 quarter = 0.25 dollar

Let the number of nickels = n

Let the number of quarters = q

Total number of coins = n + q = 30 ------(1)

The value of coins = 0.05n + 0.25q = 4.10

By dividing this equation by 0.05

n + 5q = 82 -------(2)

Now we subtract equation (2) from equation (1)

(n + 5q) - (n + q) = 82 - 30

5q - q = 52

4q = 52

q =
`(52)/(4)`

q = 13

By putting n = 13 in the equation (1)

n = 30 - 13 = 17

In 30 coins 17 are nickels and 13 are quarters.