White an inequality

Question

If company A charges a flat fee of $.15 for every card and company B charges $.10 per card plus $10.00 shipping. How many cards would you have to buy to make company B the cheaper option. Write an inequality for the answer 

Answer 1

Let x = number of cards

 

Company A charges:    $0.15x

Company B charges:    $10.00 + $0.10x

 

For company B to be the cheaper option:      ( B < A )

      $10.00 + $0.10x  <  $0.15x

      $10.00  <  $0.05x      [subtracting positive from both sides

            retains the sense of the inequality and x is positive]

        200 < x         [dividing by positive 0.05 retains sense of inequality]

        x > 200        [read in reverse to make sense]

  You would have to buy more than 200 cards for B to be cheaper.

 

Let's check:

  For 200 cards,

     Is $10.00 + $0.10(200) < $0.15(200)   ?

         $10.00 + $20.00 < $30.00   ?

            $30.00  <  $30.00   ?no, they are equal

 

  For 201 cards,

    Is $10.00 + $0.10(201) < $0.15(201)   ?

        $10.00 + $20.10 < $30.15   ?

         $30.10 < $30.15   ?yes

Answer 2

.15x > .10x + 10

Solve for x

x > 200

 

So, the smallest number of cards that would make company the cheaper option is 201.