document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=533052>Question 533052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When toni got a grade of 98 on a certain test it raised her test average by one point. But when she got a grade of 70 on her next test, her average went down by two points. How many tests did she take?\r<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 #351021 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=351021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When toni got a grade of 98 on a certain test it raised her test average by one point.<BR>\n" );
document.write( " But when she got a grade of 70 on her next test, her average went down by two points.<BR>\n" );
document.write( " How many tests did she take? <BR>\n" );
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document.write( "let n = original number of test, before the 98 test<BR>\n" );
document.write( "let a = original average of these tests<BR>\n" );
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document.write( "\"When toni got a grade of 98 on a certain test it raised her test average by one point.\"<BR>\n" );
document.write( "a + 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28na%2B98%29%29%2F%28%28n%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28na%2B98%29%29%2F%28%28n%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by (n+1)<BR>\n" );
document.write( "(n+1)(a+1) = na + 98<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "na + n + a + 1 = na + 98<BR>\n" );
document.write( "subtract na from both sides<BR>\n" );
document.write( "n + a + 1 = 98<BR>\n" );
document.write( "subtract 1 from both sides, a simple two unknown equation:<BR>\n" );
document.write( "n + a = 97<BR>\n" );
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document.write( "Note that now her average is (a+1) and the number of test taken is (n+1)<BR>\n" );
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document.write( "\" But when she got a grade of 70 on her next test, her average went down by two points.\"<BR>\n" );
document.write( "Now her average is (a+1-2) and the number of test taken is n+2<BR>\n" );
document.write( "a + 1 - 2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28na%2B98%29%2B70%29%2F%28%28n%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28%28na%2B98%29%2B70%29%2F%28%28n%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a - 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28na%2B168%29%29%2F%28%28n%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28%28na%2B168%29%29%2F%28%28n%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by (n+2)<BR>\n" );
document.write( "(n+2)(a-1) = na + 168<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "na - n + 2a - 2 = na + 168<BR>\n" );
document.write( "Subtract na and add 2 to both sides<BR>\n" );
document.write( "-n + 2a = 170<BR>\n" );
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document.write( "Use elimination here on these two equations<BR>\n" );
document.write( "-n + 2a = 170<BR>\n" );
document.write( "+n + a = 97<BR>\n" );
document.write( "---------------adding eliminates n, find a<BR>\n" );
document.write( "3a = 267<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=267%2F3 ALIGN=MIDDLE  ALT=\"267%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 89 is original average before the two test<BR>\n" );
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document.write( "Find n<BR>\n" );
document.write( "n + 89 = 97<BR>\n" );
document.write( "n = 97 - 89<BR>\n" );
document.write( "n = 8 test taken originally, then a total of 10 test were taken by Toni<BR>\n" );
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document.write( "See if that works<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2889%29%2B98%2B70%29%2F10 ALIGN=MIDDLE  ALT=\"%288%2889%29%2B98%2B70%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 88 is the final average which is 1 point below the original average of 89 </SPAN>\n" );
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