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# Word Problem Worksheets 1

Lesson Plans > Mathematics > Algebra > Word Problems

## Word Problem Worksheets 1 When students first start doing algebraic word problems, the hard part is not solving the equations; it's converting the statement(s) of the problem into equation(s) to solve. The ability to convert sentences into equations is dependent on the students' ability convert phrases into algebraic expressions. After all, an equation is nothing more than two algebraic expressions connected by an equals sign.

If your students need practice converting phrases to expressions, there is a series of practice worksheets available here: Algebraic Expressions. From the page linked, you can access the rest of the pages in the series from the links at the bottom of each page.

If your students are proficient in converting phrases to expressions, the next step is fairly simple - converting sentences to equations.

In every equation, there is a balance point - the equals sign. The information on the left-hand side of the equation balances the information on the right hand side. In the same way, if a sentence can be converted into an equation, it must also have a balance point. There are a variety of words or phrases that can function as the "balance point," but in this section, we're going to focus on a single word: is. Most often, when you find the word "is" in a sentence, you've found the balance point (the equals sign) of the equation. Students should not be led to believe that this is always the case, but it's definitely a good starting point. We'll explore other balancing words and phrases later.

So the process for converting a sentence into an equation is as follows:

• Identify the balancing word/phrase
• Identify the phrase to the left of the balance point that can be written as an algebraic expression
• Identify the phrase to the right of the balance point that can be written as an algebraic expression
• Write the two expressions with an equals sign between them.

Example: The sum of a number and 15 is 32

Solution: (The sum of a number and 15) = (32); n + 15 = 32

Example: The sum of a number and 12 is twice the number.

Solution: (The sum of a number and 12) = (twice the number); n + 12 = 2n

In the first worksheet given below, students must state the unknown, write the equation, and solve. The word "is" appears only once in each statement, and it always represents the balance point of the statement.

In the second worksheet, the balance point is always a form of the verb "to be". For example: is, was, will be.

## In This Unit

Lesson by Mr. Twitchell

## Word Problems Worksheet #1.1

For each statement below, pick a variable to represent the unknown. State what the variable represents, write the statement as an algebraic equation. Solve the equation, and answer the question.

Example:     The sum of a number and twice that number is 33
Solution:      n = the number; n + 2n = 32; n = 11

1. The sum of a number and 32 is 84. Find the number.

2. Twice the price of a book is \$12 less than the price of 4 books. Find the price of three books.

3. A number, plus three more than that number, is 81. What is the number?

4. Four more than a number is twelve less than twice the number. What is the number?

5. My age is equal to twice what my age was 15 years ago. What was my age 15 years ago?

6. A number, plus two more than twice the number, is 22 less than seven times the number. What is the number?

7. The sum of a number and ten more than that number is 120. What is the number?

8. The amount of time it takes to mow a lawn is five hours less than the amount of time it takes to mow three lawns. How much time does it take to mow two lawns?

9. The price of a dozen eggs was discounted by 35 cents. the resulting price is the same as if it had been discounted by 10%. How much does a dozen eggs normally cost?

10. A rent increase of \$32 is the same as a rent increase of 5%. How much would the rent be if it had been increased by 10%?

11. The sum of two consecutive integers is 81. What is the larger of the two integers?

12. The sum of two consecutive odd integers is 64. What is the average of the two numbers?

## Word Problems Worksheet #1.1: Answer Key

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## Word Problems Worksheet #1.2

For each statement below, pick a variable to represent the unknown. State what the variable represents, write the statement as an algebraic equation. Solve the equation, and answer the question.

Example:     Ten years ago, John was half as old as he is now. How old is he?
Solution:      j = his age; j - 10 =
1
2
j; j = 20

1. Twelve years from now, Sam will be twice his current age. How old wil he be then?

2. Five years ago, Jenn's age was 24 less than twice her current age. How old is she?

3. Half of the sum of a number and twice that number is 45. What is the number?

4. If the price of a car increases by 12%, the new price will be \$26,880. What is the original price?

5. If the price of a car decreases by 6%, the new price will be \$924 less than the original price. What is the new price?

6. Every day I walk the same distance. The distance I walked yesterday was twenty less than twice the distance I walked today. How far did I walk yesterday?

7. The sum of a number and five less than twice that number is equal to 51 more than one third of that number. What is the number?

8. My age ten years ago was four less than two thirds of my current age. How old was I ten years ago?

9. A number, plus twice that number, plus half of that number, equals 420. What is the number?

10. A train had freight cars plus two engines. When 18 freight cars were added to the train, the train's length was 250% of the original length. What was the original length of the train?

11. The difference between a number and two fifths of that number is sixteen more than half the number. What is the number?

## Word Problems Worksheet #1.2: Answer Key

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