document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "a. Find x such that the cost of each chair is the same as when Mr. Lim
\n" ); document.write( "ordered 5 chairs.\r
\n" ); document.write( "\n" ); document.write( "b. Find the number of chairs in a batch he needs to orders such that the cost
\n" ); document.write( "per chair is less than $45. \n" ); document.write( "

Algebra.Com's Answer #852026 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs,
\n" ); document.write( "the cost of each chair, $y is given by y = x2 - 14x + 80.
\n" ); document.write( "(a) Find x such that the cost of each chair is the same as when Mr. Lim
\n" ); document.write( "ordered 5 chairs.
\n" ); document.write( "(b) Find the number of chairs in a batch he needs to orders such that the cost
\n" ); document.write( "per chair is less than $45.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  If he orders 5 chairs, the cost of each chair is\r\n" );
document.write( "\r\n" );
document.write( "         5^2 - 14*5 + 80 = 35 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     To find x, we should solve this quadratic equation\r\n" );
document.write( "\r\n" );
document.write( "         x^2 - 14x + 80 = 35.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     This equation is the same as\r\n" );
document.write( "\r\n" );
document.write( "        x^2 - 14x + 80 - 35 = 0,\r\n" );
document.write( "\r\n" );
document.write( "        x^2 - 14x + 45 = 0,\r\n" );
document.write( "\r\n" );
document.write( "        (x-5)*(x-9) = 0     (after factoring).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     One root is  5 chairs  (the value we started with).\r\n" );
document.write( "\r\n" );
document.write( "     The other root is 8, which is the ANSWER to question (a).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  To answer (b), we should solve this inequality\r\n" );
document.write( "\r\n" );
document.write( "        x^2 - 14x + 80 <= 45.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Transform and simplify it\r\n" );
document.write( "\r\n" );
document.write( "        x^2 - 14x + 80 - 45 <= 0,\r\n" );
document.write( "\r\n" );
document.write( "        x^2 - 14x + 35 <= 0,\r\n" );
document.write( "\r\n" );
document.write( "      \r\n" );
document.write( "     Apply the quadratic formula to find the roots.\r\n" );
document.write( "\r\n" );
document.write( "     The roots are   = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     So, one root is   = 3.26 (approx.)  and  another root is   = 10.74 (approx.)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Function x^2 - 14x + 35  is negative between the roots.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Since we are interested to know integer values of x, they are  between 4 and 10 inclusive.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     So, the ANSWER to question (b)  is  \"integer numbers between 4 and 10 inclusive\".\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );