Question

You have 85 cents made up of nickels (5 cents) and (25 cents). You only have 9 coins. How many quarters and nickels do you have?

Answer 1

`7` nickels and `2` quarters

Explanation:

Use this table to help you visualize how to get the answer:

As you can see, start with determining the amount of each coin you have.

If you have `x` nickels and `9` coins in total, therefore you must have `9 - x` quarters.

Then determine the unit price of each coin.

Nickels are `5` cents a piece, and quarters are `25` cents a piece.

Now you have to get the total, so multiply the amount by the unit price for both coins.

Nickels:

`5x`

Quarters:

`25 (9 - x)`

Now considering this information, adding them together must add to `85` cents because that is the total amount you have. This gives us the following equation:

`5x + 25 (9 - x) = 85`

Simplify.

`5x + 225 - 25x = 85`

`-20x + 225 = 85`

`-20x = -140`

`x = 7`

This means that you have `7` nickels.

Now knowing this and that you have `9` total coins, you have to do `9 - 7` to get `2`, the amount of quarters you have.

So this is why you have `7` nickels and `2` quarters.