Question

Forty- two coins have a total value of $6.90. If the coins are all nickels and quarters, how many are nickels? And how many are quarters?

Answer 1

It has given that, total number of coins = 42 and sum of money is $6.90. coins are all nickel and quarter.

We have to find number of quarters

Solution : let number of quarter is x and number of nickel is y.

total number of coins = 42

⇒x + y = 42 .....(1)

Sum of money = $6.90

⇒amount of quarter coins + amount of nickel coins = $6.90

⇒x × $0.25 + y × $0.05 = 6.90

⇒0.25x + 0.05y = 6.90

⇒25x + 5y = 690

⇒5x + y = 138 ......(2)

Solving equations (1) and (2) we get,

5x + y - x - y = 138 - 42 = 96

⇒x = 24

therefore the number of quarters is 24.