Algebra Word Problems using Coins

Coin Word Problem
A person has 12 coins consisting of quarters and pennies. If the total amount of money is $1.32, how many of each coin are there?
quarters =
pennies =
The answer is: ?

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This test helps you practice word problems that involve algebra and two unknown quantities. Below the problem and answer you can learn how to solve this word problem. All work will be shown for each word problem answer.

How to solve a word problem:

To solve this word problem you need to find 2 unknown values, the quantity of each coin that will total the total amount of money. If we call the unknown value of the first coin X and the unknown value of the second coin Y, these are the 2 values we need to find. However, since we know the total number of coins we have, the following equation is true: Y = Total Coins - X. Therefore, if we solve for X we can easily find Y.

For example, if person has 11 coins consisting of quarters and nickels and the total amount of change is $1.75 we would start solving this word problem by letting X = the number of quarters and Y = (11 - X) = the number of nickels.

Putting this into an equation to solve for X we have:
X Quarters + Y Nickels = 1.75
25 cents * X + 5 cents Y = 1.75
25 cents * X + 5 cents * (11 - X) = 1.75

It is easier to work with whole numbers so we put all of the coins in terms of their value in cents and solve for X.
25X + 5(11 - X) = 175

Multiplying out the terms in the parentheses we get
25X + 55 - 5X = 175

Combining terms that contain X we get
20X + 55 = 175

Moving like-terms to one side of the equation we get
20X + 55 - 55 = 175 - 55
20X = 120

To reduce X by itself, we divide both sides of the equation by 20:
20X / 20 = 120 / 20
X = 6 or we have 6 quarters.

To find the number of nickels we subtract 6 from the total number of coins or we solve for Y = 11 - X = 11 - 6 = 5.

Answer: 6 quarters and 5 nickels = $1.75

If necessary, use the following table of values to solve these word problems.

Coins Cents Value Dollar Value
Penny
$0.01
Nickel
$0.05
Dime
10¢
$0.10
Quarter
25¢
$0.25
Half Dollar
50¢
$0.50
 

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Furey, Edward "Algebra Word Problems: Coins" From http://www.CalculatorSoup.com - Online Calculator Resource.