document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=432674>Question 432674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I am having complications solving two word problems involving inequalities. Please solve these and/or help me on these word problems. Thanks a lot!\r<BR>\n" );
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document.write( "1.  Find the largest pair of consecutive even integers whose sum is less than 85.<BR>\n" );
document.write( "2.  Eve's grades on three tests were 78, 93, and 63. What is the lowest grade she can get on the next test to have an average higher than 80?\r<BR>\n" );
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document.write( "Thanks again! <BR>\n" );
document.write( "Megan, 13 year old Algebra student <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 #300064 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300064\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Find the largest pair of consecutive even integers whose sum is less than 85.<BR>\n" );
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document.write( "Let the 2 consecutive even integers = x, (x+2)<BR>\n" );
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document.write( "the equation for the given statement:<BR>\n" );
document.write( "x + (x+2) < 85<BR>\n" );
document.write( "Combine like terms:<BR>\n" );
document.write( "2x + 2 < 85<BR>\n" );
document.write( "subtract 2 from both sides:<BR>\n" );
document.write( "2x < 85 - 2<BR>\n" );
document.write( "2x < 83<BR>\n" );
document.write( "Divide both sides by 2<BR>\n" );
document.write( "x < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=83%2F2 ALIGN=MIDDLE  ALT=\"83%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x < 41.5<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "40, 42, are the largest even consecutive  integer<BR>\n" );
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document.write( "Check this<BR>\n" );
document.write( "40+42 = 82<BR>\n" );
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document.write( "2. Eve's grades on three tests were 78, 93, and 63.<BR>\n" );
document.write( " What is the lowest grade she can get on the next test to have an average higher than 80?<BR>\n" );
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document.write( "Let x = her grade on the 4th test<BR>\n" );
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document.write( "The equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B78%2B93%2B63%29%2F4 ALIGN=MIDDLE  ALT=\"%28x%2B78%2B93%2B63%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > > 80<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B234%29%2F4 ALIGN=MIDDLE  ALT=\"%28x%2B234%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > > 80<BR>\n" );
document.write( "Multiply both sides by 4<BR>\n" );
document.write( "x + 234 > 4(80)<BR>\n" );
document.write( "x + 234 > 320<BR>\n" );
document.write( "Subtract 234 from both sides<BR>\n" );
document.write( "x > 320 - 234<BR>\n" );
document.write( "x > 86<BR>\n" );
document.write( "She will need at least an 87 to have an average greater than 80<BR>\n" );
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document.write( "Check this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2887%2B78%2B93%2B63%29%2F4 ALIGN=MIDDLE  ALT=\"%2887%2B78%2B93%2B63%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=321%2F4 ALIGN=MIDDLE  ALT=\"321%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 80.25, just greater than an 80 average\r<BR>\n" );
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