A collection of 36 coins consists of nickels, dimes and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin are there?

9 quarters, 12 nickels, and 15 dimes.

Step-by-step explanation:

Let's start by naming the number of quarters x.

That means that the number of nickels is x+3.

(There are three fewer quarters than nickels)

The number of dimes would be x+6.

(There are six more dimes than quarters)

We know the total number of coins is 36.

We can set up an equation.

quarters+nickels+dimes=36

x+x+3+x+6=36

Combine like terms.

3x+9=36

Subtract 9 from both sides.

3x=27

Divide both sides by 3.

x=9

There are 9 quarters.

Use given info to find the number of other coins.

9+3=12

There are 12 nickels.

9+6=15

There are 15 dimes.