document.write( "Question 479249: I need to know what the linear equation would be for the following word problem:
\n" ); document.write( "A teacher is given a $300 stipend for supplies. Company A offers a 15% discount, but Company B offers a 20% discount after the first $20 spent. \n" ); document.write( "
Algebra.Com's Answer #328387 by Theo(13342)\"\" \"About 
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you can model company A with one equation.
\n" ); document.write( "that equation would be:
\n" ); document.write( "y = .85*x
\n" ); document.write( "y is the sale price.
\n" ); document.write( "x is the retail price.
\n" ); document.write( "you cannot model company B with one equation.
\n" ); document.write( "at least i haven't been able to.
\n" ); document.write( "it requires programmed logic and 2 equations to handle it.
\n" ); document.write( "the first equation does not apply any discount up to 20 dollars.
\n" ); document.write( "the second equation applies 20% discount if the value of the order is greater than 20 dollars.
\n" ); document.write( "the question then remains as to whether the discount is applied to the whole order or just to the part of the order that is greater than 20 dollars.
\n" ); document.write( "i'll assume the 20% discount only applies to the amount over the 20 dollars spent.
\n" ); document.write( "the equation for company B would be:
\n" ); document.write( "if the retail price is less than or equal to 20 dollars than:
\n" ); document.write( "y = x
\n" ); document.write( "if the retail price is greater than 20 dollars, then:
\n" ); document.write( "y = .80 * (x-20) + 20
\n" ); document.write( "here's a small table of the difference in cost to the customer.
\n" ); document.write( "
\r\n" );
document.write( "retail price          company A sale price     company B sale price\r\n" );
document.write( "0                             0                        0\r\n" );
document.write( "20                           17                       20\r\n" );
document.write( "40                           34                       36\r\n" );
document.write( "60                           51                       52\r\n" );
document.write( "80                           68                       68\r\n" );
document.write( "100                          85                       84\r\n" );
document.write( "

\n" ); document.write( "looks like the cut-over point is when the retail price is 80 dollars.
\n" ); document.write( "we can find the cut-over price by formula.
\n" ); document.write( "for company A, S = .85x
\n" ); document.write( "for company B, S = .80(x-20) + 20
\n" ); document.write( "make .85x = .80(x-20) + 20 and you'll find the cut-over point.
\n" ); document.write( "expand this equation to get:
\n" ); document.write( ".85x = .80*x - .8*20 + 20 which becomes:
\n" ); document.write( ".85x = .80x - 16 + 20 which becomes:
\n" ); document.write( ".85x = .80x + 4
\n" ); document.write( "subtract .80x from both sides of the equation to get:
\n" ); document.write( ".05x = 4
\n" ); document.write( "divide both sides of the equation by .05 to get:
\n" ); document.write( "x = 4/.05
\n" ); document.write( "simplify this to get:
\n" ); document.write( "x = 80
\n" ); document.write( "that's the cut-over point when company B discount becomes better than company A discount.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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