A money word problem describes coins, bills, or prices and asks you to model the situation with a linear equation. Name the unknown quantity, express the remaining quantity in terms of it, and set up a total-value equation. See a worked coin example solved step by step.
Setting up a money word problem
A money word problem asks you to turn a real situation involving coins, bills, or prices into a linear equation. The trick is to name one unknown quantity, express everything else in terms of it, and write an equation for the total value.
Worked example
A jar holds 20 coins, some nickels and some quarters, worth a total of $3.20. Let n be the number of nickels. Since there are 20 coins total, the number of quarters must be 20 − n. Each nickel is worth 5¢ and each quarter 25¢, so the total value in cents is 5n + 25(20 − n).
Naming the unknown and writing the value equation for a coin problem.
Setting that equal to 320 cents and solving: 5n + 500 − 25n = 320, so −20n = −180, giving n = 9. There are 9 nickels and 11 quarters.
The general approach
Every money word problem follows the same three steps: name the unknown, write an expression for the remaining quantity, and multiply each quantity by its value before adding. This is the same modeling skill used in unknown-number word problems, distance-and-time word problems, and rectangle word problems — only the quantities being modeled change.