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PROBLEM-SOLVING USING INEQUALITIES

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					PROBLEM-SOLVING USING
    INEQUALITIES

 To solve word problems by using
   inequalities in one variable.
Find all the sets of four consecutive
even integers whose sum is between
225 and 250.
1. Define the variable:
x = smallest consecutive even integer
x + 2 = next consecutive even integer
x + 4 = third consecutive even integer
x + 6 = largest consecutive even integer
    Find all the sets all of four
    consecutive even integers whose
    sum is between 225 and 250.
2. Write an equation:

225 < x + (x + 2) + (x + 4) + (x + 6) < 250
    Find all the sets all of four
    consecutive even integers whose
    sum is between 225 and 250.
3. Solve:

225 < x + (x + 2) + (x + 4) + (x + 6) < 250

              225 < 4x + 12 < 250

  225 < 4x + 12         and     4x + 12 < 250
   213 < 4x                         4x < 238
   53.25 < x                        x < 59.5
Find all the sets all of four
consecutive even integers whose
sum is between 225 and 250.
 53.25 < x        and         x < 59.5

         X = 54 or 56 or 58

              ANSWERS:
             54, 56, 58, 60
             56, 58, 60, 62
             58, 60, 62, 64
A store is charged $5.50 each for
calculators and a delivery charge
of $25 for the order. If the store
sells the calculators for $8 each,
 how many calculators must be
 ordered and sold to produce a
        profit of the $80?
A store is charged $5.50 each for
calculators and a delivery charge of
$25 for the order. If the store sells the
calculators for $8 each, how many
calculators must be ordered and sold to
produce a profit of at least $80?

1. Define the variable:
                  c = calculators sold
A store is charged $5.50 each for
calculators and a delivery charge of
$25 for the order. If the store sells the
calculators for $8 each, how many
calculators must be ordered and sold to
produce a profit of at least $80?

2. Equation:

               8c – (5.50c + 25) > 80
A store is charged $5.50 each for calculators
and a delivery charge of $25 for the order.
If the store sells the calculators for $8 each,
how many calculators must be ordered and
sold to produce a profit of at least $80?


3. Solve:   8c – 5.50c – 25 > 80
                2.50c – 25 > 80
                    2.50c > 105
                        c > 42     at least 42 calculators
1.    John's scores in his first four tests were 72, 74, 89,
      91. What will he have to score on his next test to
      obtain a B- average?

Define the Variable:
                 x = fifth test score
Write an inequality:
               72  74  89  91  x
                                      79.5
                         5
Solve:        326  x
                        79.5
                 5
              326  x  397.5
              x  71.5     John must score an 71.5%
 2. The four sides of a square are increased by 10 cm, 20 cm, 30
     cm and 40 cm respectively. The perimeter of the resulting
   quadrilateral is between five and six times the perimeter of the
original square. What can you conclude about the length of the side
                        of the original square?

                                         x + 40
   Define the variable:
                           x + 30                       x + 10
                 x
                                       x + 20
    Write an inequality:              16x < 100 and -20x < -100
                                        x < 6.25       x>5
   20x < 4x + 100 < 24x
                            The original square had a length of
    Solve:                  between 5 and 6.25 cm.
   20x < 4x + 100 and 4x + 100 < 24x
3. The cable company offers two types of service. With plan A, you can get
basic cable per month for $42.50 and an additional $17.50 for all of the
premium channels. With plan B, you can get basic cable for $42.50 with
additional premium channels for a $1.25 per channel. How many premium
channels which you need to order with plan B before plan A would become
cheaper?


    Define the variable.                Solve.

    c = number of                         60 < 42.50 + 1.25c
    premium channels
                                          17.50 < 1.25c
    ordered
                                          14 < c
    Write an inequality.

    42.50 + 17.50 < 42.50 + 1.25c         You will need to order 15
                                          additional premium channels
                                          for plan A to be cheaper.
Pg. 71 2, 3, 4, 6, 7, 11

				
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