Algebraic Expressions and Word Problems

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Examples, solutions, videos, worksheets, games and activities to help Algebra 1 or grade 7 students learn how to write algebraic expressions from word problems.

Beginning Algebra & Word Problem Steps

  1. Name what x is.
  2. Define everything in the problem in terms of x.
  3. Write the equation.
  4. Solve the equation.


  1. Kevin’s age is 3 years more than twice Jane’s age. The sum of their ages is 39. How old is Kevin and Jane?
  2. The difference between two numbers is 7. Find the two numbers if the larger number is three times the smaller.
  3. Mary and Jim collect baseball cards, Mary has 5 more than 3 times as many cards as Jim. The total number of cards they both have is 253. How many cards does Mary have?

How to writing a word problem as an algebraic expression?
Last week, Shaun had half as many computer games as Johan. He purchased 3 more games this week. Write an expression that represents the number of games Shaun now has if j represents the number of games that Johan has?

Algebraic Word Problem
Devon is going to make 3 shelves for her father. She has a piece of lumber 12 feet long. She wants the top shelf to be half a foot shorter than the middle shelf, and the bottom shelf to be half a foot shorter than twice the length of the top shelf. How long will each shelf be if she uses the entire 12 feet of wood?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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