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Practice Problems for Mystery Numbers:

1.    Five times an unknown number decreased by 7 is 43. Find the number.
        Answers           Solutions

2.    When 4 is subtracted from half of an unknown number the result is 17. Find the      number.
            Answers           Solutions

3.    The sum of 6 and twice an unknown number is 32. Find the number.
        Answers           Solutions

4.    Fifty-two is 2 less than 6 times a number. Find the number
        Answers        Solutions.

5.    Eight less than 5 times a number is 57. Find the number.
        Answers          Solutions
 

6.    Eight less than 5 times a number is four more than 8 times the number. Find the number.
        Answers           Solutions

7.    The sum of two numbers is 30. Three times the first plus twice the second number is 72. Find the numbers.
        Answers        Solutions

8.    The sum of two numbers is 40. One number is one more than twice the other. Find the numbers.
        Answers        Solutions

Answers:

1.    10

2.    42

3.    13

4.    9

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5.    13

6.    -4

7.    12 ,18

8.    27, 13

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Solutions:

1.     Five times an unknown number decreased by 7 is 43. Find the number.
 a.    Read the problem several times. Guess the answer. You might be able to get this one with just a couple of guesses.

b.    Define x, usually to answer the question.
Let x = the number.
c.     Label other unknown quantities in terms of x.
This step is not necessary on this problem.
d.    Form the equation.
5x – 7 = 43
e.    Solve the equation.
5x – 7 = 43
5x = 50
x = 10
f.     Anwer the question.

          The number is 10. Check to see that 5 times this number decreased by 7 is 43.

    2.    When 4 is subtracted from half of an unknown number the result is 17. Find the number.

        a.    Read the problem several times. Guess.
        If we guess 40 then half of 40 is 20 and subtracting 4 from 20 leaves us with 16…pretty close.
        b.    Define x, usually to answer the question.
        Let x = the number.
        c.    Label other unknown quantities in terms of x.
        There are no other unknowns in this problem.
        d.    Form the equation.

         e.    Solve the equation.

     
    f.     Answer the question.

    Check to see that 42 behaves as advertised.

    3.    The sum of 6 and twice an unknown number is 32. Find the number.
    a.    Read the problem several times. Guess.

     
    Write your guess down now. If it is too far off, make a new improved guess.

    b.    Define x, usually to answer the question.

    Let x = the number.

    c.    Label other unknown quantities in terms of x.

    There are no other unknown quantities in this problem.

    d.    Form an equation.

    2x + 6 = 32

    e.    Solve the equation.

    2x + 6 = 32

    2x = 26

    x = 13

    f.    Answer the question.

    Check to see that the number 13 behaves as advertised.

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4.     Fifty-two is 2 less than 6 times a number. Find the number.
     a.    Read the problem several times. Guess the answer.
      It can be difficult to guess out of the blue, but lets try a guess of 10. Now 6 times 10 is 60 and 2 less than 60 is not 52 but    it’s not that far off. Our true answer then should be less than 10..
      b.  Define x, usually to answer the question.
        Let x = the number.
      c.    Label other unknown quantities in terms of x.
        In this problem there are no other unknown quantities.
      d.    Form an equation.
        52 = 6x – 2. Some people are tempted to try 52 = 2 – 6x. Be especially careful when translating subtraction.
      e.    Solve the equation.
        52 = 6x – 2
        54 = 6x
        9 = x
      f.    Answer the question. The mystery number is 9. The guess was pretty close.
5.     Eight less than 5 times a number is 57. Find the number.

     a.    Read the problem several times. Guess.

     b.    Define x, usually to answer the question.
     Let x = the number.
     c.    Label unknown quantities in terms of x.
      There are no other unknowns in this problem.
      d.    Form an equation.
      5x – 8 = 57
      e.    Solve the equation.
      5x – 8 = 57
      5x = 65
       x = 13
      f.    Answer the question.
      To check, 5 times 13 is 65 and 8 less than 65 is 57.

6.     Eight less than 5 times a number is four more than 8 times the number. Find the number.

    a.    Read the problem several times. Guess.
    This would be a rather difficult guess, but give it a try anyway.
    b.    Define x, usually to answer the question.
    Let x = the number.
    c.    Label other unknown quantities in terms of x.
    There are no other unknown quantities.
    d.    Form an equation.
    5x – 8 = 8x + 4
    e.    Solve the equation.
    5x – 8 = 8x + 4
    -3x = 12
      x = -4
     f.    Answer the question.
     Does the number behave as advertised?
7.     The sum of two numbers is 30. Three times the first plus twice the second number is 72. Find the numbers.
      a.    Read the problem several times. Guess.
       In our guess, the numbers have to add to 30. Try 14 and 16. Can you do better?
      b.    Define x, usually to answer the question.
        Let x = the first number.
      c.    Label other unknown quantities in terms of x.
       Let 30 – x = the other number. Since the numbers have to add to 30, if we subtract one number (x) from 30 we will get an   algebraic name for the other.
      d.    Form an equation.
      3x + 2(30 – x) = 72
      e.    Solve the equation.
      3x + 60 – 2x = 72
      x = 12
      f.    Answer the question.
      If x = 12 then 30 – x = 30 – 12 = 18. The two numbers are 18 and 12.
8.    The sum of two numbers is 40. One number is one more than twice the other. Find the numbers.
     a.    Read the problem several times. Guess.
     You may be able to get this one on the first guess. Even if you can get the correct answer with the first or second guess, practice your algebra. You will need it as guessing gets harder.
     b.    Define x, usually to answer the question.
     Let x = larger number
     c.    Label other unknown quantities in terms of x.
     Let 40 – x = the other number.
     d.    Form an equation.
     x = 2(40 – x) + 1
     e.    Solve the equation.
     x = 2(40 – x) +1
     x = 80 – 2x + 1
     3x = 81
      x = 27
     f.    Answer the question.
     If x = 27 then 40 – x = 40 – 27 = 13.                Back To The Top

 
   
 
 
 
 
 

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