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Algebra Word Problems Using Coins

Coin Word Problem
A person has 12 coins consisting of quarters and dollar coins. If the total amount of money is $8.25, how many of each coin are there?

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This calculator helps you practice word problems that involve algebra and two unknown quantities. Use paper to do the math for the given problem, then input your answers here and click the Calculate button. The calculator will evaluate your answers and then show the work so you can learn how to solve the word problem.

How to solve this algebra word problem:

To solve this word problem you need to find 2 unknown values: the quantity of each coin that will add up to the total dollar amount. 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, the following equation is true: Y = Total Coins - X. Therefore, if we solve for X we can easily find Y.

For example, if a person has 11 coins consisting of quarters and nickels, and the total dollar amount 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

Divide both sides of the equation by 20:
20X / 20 = 120 / 20
X = 6, which means 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

This table of coin values can help you solve these word problems.

Cents Value
Dollar Value
Half Dollar

Cite this content, page or calculator as:

Furey, Edward "Algebra Word Problems Using Coins"; from http://www.calculatorsoup.com - Online Calculator Resource.

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