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Practice Problems for Consecutive Numbers
 

9.  The sum of two consecutive even integers is 106. Find the integers. Answers

    Solution
10.   The sum of two consecutive odd integers is –40. Find the integers. Answers
Solutions

11.    Find three consecutive integers if twice the largest is 16 less than three times the smallest.   Answers           Solutions
 
 
 

Answers 1-3:

9.    52 and 54   Solution

10.    -21 and -19.     Solution

11.    20, 21,and 22    Solution
 

Solutions 1- 3:

9.    The sum of two consecutive even integers is 106. Find the integers.
 

                a.    Read the problem several times. Guess.

       
      The integers have to be in the neighborhood of 106 divided by 2.

      b.     Define x, usually to answer the question.

      Let x = the first even integer.

      c.     Label other unknown quantities in terms of x.

      Let x + 2 = the second even integer.

      d.    Form an equation.

      x + (x + 2) = 106

      e.     Solve the equation.

      x + (x + 2) = 106

      2x + 2 = 106

      2x = 104

      x = 52

      f.     Answer the question.

If x = 52, then x + 2 = 54.                                                     Back To The Top

10.     The sum of two consecutive odd integers is –40. Find the integers.

a. Read the problem several times. Guess.

      What’s your guess? Write it down and check it later.

      b.     Define x, usually to answer the question.
       

      Let x = the first odd integer.

      c. Label other unknown quantities in terms of x.
       

      Let x + 2 = the second odd integer.

      d.     Form an equation.
       

      x + (x + 2) = -40

      e.     Solve the equation.
       

      2x + 2 = -40

      2x = -42

      x = -21

      f.      Answer the question.

If x = -21, then x + 2 = -19. Note that the two integers do add to –40.

11.   Find three consecutive integers if twice the largest is 16 less than three times the smallest.

a.     Read the problem several times. Guess.

      This is a tough one for guessing. Better pull out the algebra.

      b.     Define x, usually to answer the question.

      Let x = the first integer

      c.     Label other unknown quantities in terms of x.
       

      Let x + 1 = the second integer.

      Let x + 2 = the third integer.

      d.     Form an equation.
       

      2(x + 2) = 3x - 16

      e.     Solve the equation.
       

      2(x + 2) = 3x – 16

      2x + 4 = 3x – 16

      4 = x – 16

      20 = x

      f.    Answer the question.

If the first integer is 20 then the next two will be 21 and 22.                                       Back To The Top
 
 
 
 

Created by:  Willette  Hackney
Date:    12/16/00
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