A collection of 109 coins is made up of quarters, dimes, and nickels. There are 7 fewer dimes than quarters and 3 less than five times as many nickels as dimes.Find the amount of the collection

There are 22 quarters, 15 dimes and 72 nickels.

Step-by-step explanation:

The number of coins in the collection is 109.

Let the number of quarters = x

Let the number of dimes = y

Let the number of nickels = z

Therefore:

x + y + z = 109 (1)

There are 7 fewer dimes than quarters. This means that:

y = x - 7

=> x = y + 7

There are 3 less than five times as many nickels as dimes. This means that:

z = 5y - 3

Let us write equation (1) in terms of y to make it simpler to solve:

y + 7 + y + 5y - 3 = 109

Collecting like terms:

7y + 4 = 109

=> 7y = 105

y = 105 / 7

y = 15

Therefore:

x = 15 + 7 = 22

z = (5 * 15) - 3

z = 75 - 3 = 72

Hence, there are 22 quarters, 15 dimes and 72 nickels.

To confirm, 22 + 15 + 72 = 109