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One number is one more than twice another. Their sum is −5 . Find the numbers.

−2 , −3

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One number is six more than five times another. Their sum is six. Find the numbers.

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The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.

4, 10

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The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.

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The sum of two consecutive integers is 77. Find the integers.

38, 39

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The sum of two consecutive integers is 89. Find the integers.

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The sum of two consecutive integers is −23 . Find the integers.

−11 , −12

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The sum of two consecutive integers is −37 . Find the integers.

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The sum of three consecutive integers is 78. Find the integers.

25, 26, 27

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The sum of three consecutive integers is 60. Find the integers.

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Find three consecutive integers whose sum is −36 .

−11 , −12 , −13

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Find three consecutive integers whose sum is −3 .

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Find three consecutive even integers whose sum is 258.

84, 86, 88

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Find three consecutive even integers whose sum is 222.

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Find three consecutive odd integers whose sum is 171.

55, 57, 59

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Find three consecutive odd integers whose sum is 291.

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Find three consecutive even integers whose sum is −36 .

−10 , −12 , −14

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Find three consecutive even integers whose sum is −84 .

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Find three consecutive odd integers whose sum is −213 .

−69 , −71 , −73

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Find three consecutive odd integers whose sum is −267 .

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Everyday math

Sale Price Patty paid $35 for a purse on sale for $10 off the original price. What was the original price of the purse?

$45

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Sale Price Travis bought a pair of boots on sale for $25 off the original price. He paid $60 for the boots. What was the original price of the boots?

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Buying in Bulk Minh spent $6.25 on five sticker books to give his nephews. Find the cost of each sticker book.

$1.25

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Buying in Bulk Alicia bought a package of eight peaches for $3.20. Find the cost of each peach.

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Price before Sales Tax Tom paid $1,166.40 for a new refrigerator, including $86.40 tax. What was the price of the refrigerator?

$1080

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Price before Sales Tax Kenji paid $2,279 for a new living room set, including $129 tax. What was the price of the living room set?

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Writing exercises

What has been your past experience solving word problems?

answers will vary

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When you start to solve a word problem, how do you decide what to let the variable represent?

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What are consecutive odd integers? Name three consecutive odd integers between 50 and 60.

Consecutive odd integers are odd numbers that immediately follow each other. An example of three consecutive odd integers between 50 and 60 would be 51, 53, and 55.

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What are consecutive even integers? Name three consecutive even integers between −50 and −40 .

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has four rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “approach word problems with a positive attitude,” use a problem solving strategy for word problems,” and “solve number problems.” The rest of the cells are blank

If most of your checks were:

…confidently. Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!

…with some help. This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential—every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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