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Word Problem Worksheets 2

Lesson Plans > Mathematics > Algebra > Word Problems
 

Word Problem Worksheets 2

In the previous word problem worksheets, students saw sentences in which the balance point of the word problem statement was the verb "to be." For example:

  • The sum of two numbers is 17.
  • John's age ten years ago was 30.
  • In five years, the population will be 24,000.

It was mentioned that the balance point will not always be the verb "to be," and in the next section, we'll deal with a few of those examples. Before we get there, though, there's another issue that students often struggle with: sometimes the verb "to be" shows up multiple times in a single sentence. Except in rare cases*, a sentence does not have two balance points, which means students have to identify from the structure of the sentence which word is the balance point. Some students intuitively grasp this, and others do not. The process of recognizing the balance point is somewhat grammatical in nature, so students who have a good grasp on the English language will do better than students who do not.

Here is an example of a sentence which contains the verb "to be" twice, but converts into a single equation:

  • When Martha's score is increased by 17, the result is 94.

Many students will intuitively grasp that the second "is" represents the balance point. For the students who don't intuitively grasp this, there are two things you can point out which will help the student recognize which is the balance point.

  • While the second "is" functions as a linking verb (connecting the first part of the sentence to the second), the first "is" is not an entire verb phrase; it is a helping verb tied to the verb "to increase." Thus, the actual verb phrase is "is increased." If the verb "to be" appears as a helping verb connected to another verb, it cannot be the balance point.
  • The word "is" in the first part of the sentence is part of a subordinate clause: "When Martha's score is increased by 17." How do you recognize a subordinate clause? A subordinate clause will begin with a subordinate conjunction. Subordinate conjunctions are words like: when, if, after, because, before, until, and where.

If you recognize either of these conditions:

  • "to be" is a helping verb
  • "to be" is part of a subordinate clause

That verb is not the balance point of the equation.

The subordinate clause will often tell you something that is being done to the unknown. In the example above, Martha's score is increased by seventeen, so that subordinate clause, as a standalone phrase, can be represented by the expression M + 17.

In the first worksheet below, students are required to find and circle the balance point of the sentence. In the second worksheet, students are also required to solve the equation.

* An example of a sentence with multiple balance points would be something like this: "The sum of two numbers is 13, which is also nine more than the product of the two numbers." This sentence actually converts into more than one equation: x + y = 13 and xy + 9 = 13

Additionally, a subordinate clause can, in some circumstances, provide you with a second balance point, leading to two equations. For example: "Although my age is twice David's, the sum of our ages is only 45." This sentence actually gives us two equations: a = 2d and a + d = 45


In This Unit

Lesson by Mr. Twitchell

Handouts/Worksheets

Word Problem Worksheet #2.1

For each statement below, circle the balance point (the word or phrase that represents an equality). Convert the statement to an equation.

  1. When a number is increased by 20, the result is 50.

     
  2. If twelve is subtracted from Bernie's age, the result is 20.

     
  3. If two numbers are added together, the result is five more than if they were subtracted.

     
  4. After the price is increased by 5%, the new price is $32.

     
  5. Because the price was decreased by $7.00, its price was $17.

     
  6. Since my salary was increased by $3,200, it is now $38,500.

     
  7. Until forty-eight books were stolen, my library's book count was 420 books.

     
  8. Twenty-one will be the result when a number is added to twice itself.

     
  9. When two numbers are added, the result will be the same as if they were multiplied.

     
  10. When five is added to the sum of two numbers, the result is 72.

     
  11. The sum of my number and the result when twelve is added to my number is 45.

     
  12. After the price was increased by 5%, it was decreased by $20. The new price was $74.5.

     
  13. My number is the result when your number and Bill's number are added together.

     
  14. If I was four years younger than I am, I would be twice as old as I would be if I was 20 years younger than I am.

     
  15. Kevin's age is twice what it was when he was 15 years younger.

     

Word Problem Worksheet #2.1: Answer Key

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Word Problem Worksheet #2.2

For each statement below, write and solve an equation. Answer the question.

  1. When sixteen is added to my number, the result is 24. What is my number?

     
  2. If the price is increased by 20%, the new price will be $400 more than it was. What is the new price?

     
  3. When a number is added to three times itself, the result is the same as if the number had been doubled and 23 added to the result. What is the number?

     
  4. If half of my pencils were stolen, I would still have twice as many as I would if 45 pencils were stolen. How many pencils did I have before the theft?

     
  5. When a number is added to itself, and six is subtracted from the result, the result is 74. What is the number?

     
  6. Before the price was decreased by 5%, it was $120 more than it is now.  What is the new price?

     
  7. When seventeen is added to a number, the result is seventeen less than twice the number. What is the number?

     
  8. If a number is decreased by thirteen, and then the result is tripled, the result is 72. What is the number?

     
  9. My bill is increased by 5%, and then it is decreased by $30. The result is the same as if it had simply been decreased by $10. What was my final bill?

     
  10. If 12 is added to my score, and then the resulting score is divided by two, and then 41 is added, the result is the same as my original score. What is my score?

     
  11. To a certain number, four more than that number is added, the result is divided by two, and the final result is equal to 22. What is the number?

     
  12. Three consecutive integers are added together, and 43 is subtracted; the result is three more than the middle number. What is the largest of the three numbers?

     

Word Problem Worksheet #2.2: Answer Key

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