document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=210910>Question 210910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A local deprtment store is having a sale in which you receive $30  off any purchase over $50. A competing store is offering 30% off all purchases over $50. Write and graph two equations that describe the prices at both stores. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159335 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> store A is giving $30 off any purchase >= $50.00<BR>\n" );
document.write( "store B is giving 30% off all purchases >= $50.00<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let x = amount of purchase over 50 dollars.<BR>\n" );
document.write( "let y = total amount paid by customer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "for store A:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = x + 50 - 30 which becomes:<BR>\n" );
document.write( "y = x + 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "for store B:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = .7*(x+50)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "no discount:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = (x+50)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in the following graph:<BR>\n" );
document.write( "the slanted line that crosses the y axis on top of the other slanted lines is the line that represents the purchase price without any discounts.<BR>\n" );
document.write( "the slanted line that crosses the y axis in between the top slanted line and the bottom slanted line is the line that represents the purchase price with a 30% discount for all purchases over $50.00<BR>\n" );
document.write( "the slanted line that crosses the y axis below the other slanted lines is the line that represents the purchase price with a $30.00 discount on all orders over $50.00<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x represents purchase price over $50.00<BR>\n" );
document.write( "discount starts at $50.00<BR>\n" );
document.write( "y represents the purchase price including any applicable discounts.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "when x = 0:<BR>\n" );
document.write( "y = $50.00 without a discount.<BR>\n" );
document.write( "y = $20.00 with a $30.00 discount.<BR>\n" );
document.write( "y = $35.00 with a 30% discount.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "when x = $409.00:<BR>\n" );
document.write( "y = $459.00 without a discount.<BR>\n" );
document.write( "y = $429.00 with a $30.00 discount.<BR>\n" );
document.write( "y = $321.30 with a 30% discount.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the larger the purchase price, the better the discount with the 30% off the total purchase price.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the following graph shows the relationships expressed above.<BR>\n" );
document.write( "horizontal lines represent the total purchase price at x = $409.00.<BR>\n" );
document.write( "vertical line represents x = $409.00<BR>\n" );
document.write( "intersection of the horizontal with the vertical lines show the values for y when x = $409.00 for the different discounts shown above.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-50%2C500%2C-50%2C500%2C%28x%2B20%29%2C.7%2A%28x%2B50%29%2Cx%2B50%2C1000000%2F%28x-409%29%2C321.3%2C429%2C459%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "next graph shows the tradeoff point where 30% discount starts getting better than $30.00 discount.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the point where the 30% discount starts getting better than the $30.00 discount is when the total purchase price over $50.00 equals $50.00<BR>\n" );
document.write( "the total purchase price without a discount equals $100.00 as indicated in the second graph below.<BR>\n" );
document.write( "the total purchase with a $30.00 discount equals $70.00<BR>\n" );
document.write( "the total purchase with a 30% discount equals $70.00<BR>\n" );
document.write( "after that the 30% discount provides the most savings as evidenced by the lower total purchase price when x > 50.<BR>\n" );
document.write( "the horizontal lines in the second graph below show the $100 purchase price without a discount and a $70 purchase price with either discount.  this is at the point where the vertical line shows x to be $50.00<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-50%2C100%2C-50%2C200%2C%28x%2B20%29%2C.7%2A%28x%2B50%29%2Cx%2B50%2C1000000%2F%28x-50%29%2C70%2C100%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );