One-Step & Two-Step Equation Word Problems

Examples, solutions, videos, worksheets, stories, and songs to help Grade 8 students learn how to solve one-step and two-step equation word problems.

Learning how to solve word problems is a very important skill in Algebra.
In this lesson, we will learn how to solve one-step equation and two-step equation word problems.

The following diagram gives some examples of solving two-step word problems. Scroll down the page for more examples and solutions of two-step word problems.

Algebra Worksheets
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One Step Equation Word Problems

Solving One-Step Word Problems

1. Define the variable
   
2. Write the equation
   
3. Solve the equation
   

Examples:

1. One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels. Define a variable. Then write and solve an equation to find how many bagels there are in the bakery.
   
2. The Parker family drove a total of 180 miles on their road trip. The distance is 1.5 times the distance they rode on the first day. How many miles did the Parker family drive on the first day?
   
3. Latoya’s softball team won 75% or 18 of its games. Define a variable then write and solve an equation to determine the number of games the team played.
   
4. Joe used 2/5 of his savings to buy a $250 headphone. How much did he have in his savings before purchasing the headphones?

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Example:
How many packages of diapers can you buy with $40 if one package costs $8?

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Examples:

1. A number decreased by 14 is -46. Find the number.
   
2. The sum of a number and 67 is -34. Find the number.
   
3. Twelve times a number is 96. What is the number?
   
4. One half of a number is 15. What is the number?
   
5. Tom paid $53.50 for 5 baseball tickets. What is the cost of each ticket?

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Two Step Equation Word Problems

Solving work problems that have two step equations.
Writing Let Statements, Verbal and Algebraic Models, Solving the Equation, Writing the Solution as a Sentence.

Examples:

1. There are 42 more red marbles in a jar than white marbles. If there are 238 marbles in the jar, how many are red, how many are white?
   
2. The sum of two numbers is 139. The second number is one more than twice the first. What are the two numbers?
3. A board ten feet long is cut into 2 pieces. One piece is three feet longer than the other. Find the length of both pieces.

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Two Step Equation Word Problems and Expressions

Expressions:

1. Three times a number divide by 5
   
2. Four more than two times a number
   
3. 6 times the sum of a number and 9
   
4. Five times the sum of twice a number and 8
   Equations:
   
5. Two thirds of a number is 24. Find the number
   
   Examples:
   
6. Six diminished by 1/3 of a number is 12. Find the number.
   
7. Four-fifths of a number decreased by two is 18. Find the number.

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More Two Step Word Problems
Examples:

1. Six more than five times the number is the same as 15 more than two times a number. Find the number.
   
2. Four less than seven times a number is is the same as 20 more than 3 times the number. Find the number.
   
3. Two times a number and 15 is the same as 43 decreased by 5 times a number. Find the number.
   
4. Twenty-eight decreased by 6 times a number is the same as the number. Find the number.

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Two-Step Equation Word Problems
Example:
You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?

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Solving a two step equation word problem

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