Topic

Money related questions in linear equations

My Progress

Pug Score

0%

Best Streak

0 in a row

Study Points

+0

Unlock Full Access
Adaptive practice
Video lessons

Read

Money Word Problems

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.

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).

Setting up a money word problem A collection of 20 coins, some nickels and some quarters, is worth 3 dollars and 20 cents. If n is the number of nickels, then 20 minus n is the number of quarters. The equation is 5 times n, plus 25 times the quantity 20 minus n, equals 320 cents. The problem 20 coins (nickels + quarters) worth 320 cents total. Let n = number of nickels, so 20 − n = number of quarters. Setting up the equation 5n + 25(20 − n) = 320 5n + 500 − 25n = 320 −20n = −180 → n = 9
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.

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.

Related lessons