# 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?

Feb 12, 2017

$7$ nickels and $2$ quarters

#### Explanation:

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:

$5 x$

Quarters:

$25 \left(9 - x\right)$

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:

$5 x + 25 \left(9 - x\right) = 85$

Simplify.

$5 x + 225 - 25 x = 85$

$- 20 x + 225 = 85$

$- 20 x = - 140$

$x = 7$

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.