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?

1 Answer
Feb 12, 2017

Answer:

# 7 # nickels and # 2 # quarters

Explanation:

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