SOLUTION: Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs, the cost of each chair, $y is given by y = x^2 - 14x + 80. a. Find x such that the cost of ea

Question 1165818: Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs, the cost of each chair, $y is given by y = x^2 - 14x + 80.
a. Find x such that the cost of each chair is the same as when Mr. Lim
ordered 5 chairs.
b. Find the number of chairs in a batch he needs to orders such that the cost
per chair is less than $45.
Answer by ikleyn(52779) (Show Source): You can put this solution on YOUR website!
.
Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs,
the cost of each chair, $y is given by y = x2 - 14x + 80.
(a) Find x such that the cost of each chair is the same as when Mr. Lim
ordered 5 chairs.
(b) Find the number of chairs in a batch he needs to orders such that the cost
per chair is less than $45.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(a)  If he orders 5 chairs, the cost of each chair is

         5^2 - 14*5 + 80 = 35 dollars.


     To find x, we should solve this quadratic equation

         x^2 - 14x + 80 = 35.


     This equation is the same as

        x^2 - 14x + 80 - 35 = 0,

        x^2 - 14x + 45 = 0,

        (x-5)*(x-9) = 0     (after factoring).


     One root is  5 chairs  (the value we started with).

     The other root is 8, which is the ANSWER to question (a).



(b)  To answer (b), we should solve this inequality

        x^2 - 14x + 80 <= 45.


     Transform and simplify it

        x^2 - 14x + 80 - 45 <= 0,

        x^2 - 14x + 35 <= 0,

      
     Apply the quadratic formula to find the roots.

     The roots are   = .


     So, one root is   = 3.26 (approx.)  and  another root is   = 10.74 (approx.)


     Function x^2 - 14x + 35  is negative between the roots.


     Since we are interested to know integer values of x, they are  between 4 and 10 inclusive.


     So, the ANSWER to question (b)  is  "integer numbers between 4 and 10 inclusive".

Solved.

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