Online Calculators

Algebra Word Problems Using Coins

Coin Word Problem
A person has 12 coins consisting of dimes and dollar coins. If the total amount of money is $9.30, how many of each coin are there?

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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" at https://www.calculatorsoup.com/calculators/wordproblems/algebrawordproblem1.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: October 7, 2023

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