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Word Problem Worksheets 3

Lesson Plans > Mathematics > Algebra > Word Problems
 

Word Problem Worksheets 3

In a previous lesson, students were taught that if a sentence can be turned into an equation, it must have a 'balance point' - a word or phrase that indicates that two things are equal to each other.  In many (though not all) cases, that balance point is a form of the verb "to be," as in the following examples:

  • The sum of two numbers is 15
  • Ten years ago, John was
    3
    4
    as old as he is now.
  • If the price of an item increases by 12%, the new price will be $18.

The verb "to be" does not always appear as the balance point, however. Examples of other words that can also be used as the balance point include

  • costs
  • equals
  • gives
  • yields
  • sells for/sold for

This is not an exhaustive list; it is merely some of the most common words. Students will sometimes struggle with finding the balance point of a sentence, if the sentence does not include the verb "to be." If they have a hard time finding that balance point, I encourage them to rewrite the sentence in such a way that it does include the word "is." For example:

  • "A table and a sofa costs $1500," can be rewritten as: "The cost of a table, plus the cost of a sofa, is $1500"
  • "Two numbers added together yields 15," can be rewritten as "The sum of two numbers is 15."
  • "Two packs of gum sell for $3.00," can be rewritten as "The cost of two packs of gum is $3.00."

For many students, the process of rewording a sentence is unnecessary; they intuitively make the leap to the right word. For other students, that leap is not obvious, and this rewriting process is helpful.

In the first worksheet, students are required to rewrite a sentence so that it uses the verb "to be" as the balance point. If you don't need your students to practice this process, move on to the second worksheet which requires solving equations.


In This Unit

Lesson by Mr. Twitchell

Handouts/Worksheets

Word Problems Worksheet #3.1

For each statement below, rewrite the sentence so it uses a form of the verb "to be" as its balance point. Write the statement as an algebraic equation. 

Example:     Jack's age and Mac's age add to 17.
Solution:      The sum of Jack's and Mac's ages is 17. j + m = 17

  1. An apple and five oranges costs $6.20.


     
  2. A doubled recipe yields 24 muffins.


     
  3. Nine is added to twice a number, resulting in a value of 72.


     
  4. Seventeen and a number add to 84.


     
  5. A number, plus twice that number results in a sum of 33.


     
  6. A number and four more than that number multiply to 60.


     
  7. Bill's age two years ago and John's age next year add to 72.


     
  8. When my rent was increased by $74, I started paying $480 per month.


     
  9. 30% inflation results in a $7.20 increase in price.


     
  10. Suzy sold 20 lemonades and 30 candy bars for $65.


     

Word Problems Worksheet #3.1: Answer Key

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Word Problems Worksheet #3.2

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

Example:    A number and four more than that number add to 31. What is the number?
Solution:     n + n + 4 = 31; n = 14

  1. Jack pays $20.00 for twelve plums, and receives 2.12 in change. How much would 5 plums cost?

     
  2. If I lost 24 paperclips, I would still have three fifths of my paperclips. How many paperclips would I have?

     
  3. For a meal plus a 15% tip, I paid $20.93 more than I would have if the meal had been half priced, and I hadn't paid a tip. What was the tip amount?

     
  4. The yield of a recipe is increased by 24 pancakes by tripling it. How many pancakes would have been produced from a doubled recipe?

     
  5. Summing three consecutive odd integers results in 74 more than the middle integer. What is the largest of the three integers?

     
  6. My age, plus my age in 20 years, sum to 92. How old will I be next year?

     
  7. A number is added to two less than four times the number, resulting in twice the number. What is the number?

     
  8. A number and seven more than the number multiply to the number squared, increased by 77. Find the number.

     
  9. The length of a wall is increased by a factor of
    3
    2
    , and then by 30 additional feet, resulting in a wall 204 feet long. How long was the wall before its length was increased?

     
  10. A number and three less than that number divide to 3. What is the number?

     

Word Problems Worksheet #3.2: Answer Key

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