document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151784>Question 1151784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Susan has a $100 gift card to her favorite restaurant. Each day, she uses her gift card to buy the same lunch for $8.50. Bret has a $75 gift card to the same restaurant. His lunches cost $6 each. Write an inequality to find what number of lunches Susan’s gift card balance will be greater than Bret’s gift card balance.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773987 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=773987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> her balance is equal to 100 - 8.50 * x<BR>\n" );
document.write( "his balance is equal to 75 - 6.00 * x<BR>\n" );
document.write( "x is the number of lunches.\r<BR>\n" );
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document.write( "her balance will be greater than his when 100 - 8.50 * x > 75 - 6.00 * x.\r<BR>\n" );
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document.write( "subtract 75 from both sides of this inequality and add 8.50 to both sides of this inequality to get:<BR>\n" );
document.write( "100 - 75 > 8.50 * x - 6.00 * x<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "25 > 2.50 * x<BR>\n" );
document.write( "divide both sides of this inequality by 2.5 to get:<BR>\n" );
document.write( "25 / 2.5 > x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "10 > x<BR>\n" );
document.write( "if 10 is greater than x, than x must be smaller than 10, therefore the inequality can be written as:<BR>\n" );
document.write( "x < 10\r<BR>\n" );
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document.write( "her balance is greater than his as long as the number of lunches is less than 10.<BR>\n" );
document.write( "their balance will be equal when x = 10.<BR>\n" );
document.write( "his balance will be greater than her when x > 10\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = 5:<BR>\n" );
document.write( "her balance is 100 - 8.50 * 5 = 57.5<BR>\n" );
document.write( "his balance is 75 - 6.00 * 5 = 45<BR>\n" );
document.write( "her balance is greater.\r<BR>\n" );
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document.write( "when x = 11:<BR>\n" );
document.write( "her balance is 100 - 8.50 * 11 = 6.5<BR>\n" );
document.write( "his balance is 75 - 6.00 * 11 = 9<BR>\n" );
document.write( "his balance is greater.\r<BR>\n" );
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document.write( "when x = 10:<BR>\n" );
document.write( "her balance is 100 - 8.50 * 10 = 15<BR>\n" );
document.write( "his balance is 75 - 6.00 * 10 = 15<BR>\n" );
document.write( "their balances are the same.\r<BR>\n" );
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