document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305760>Question 305760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a business studies test, 30 more students passed than the number of those that failed. In the next test, 7 students who passed the first test, failed & 1/3 of those who failed passed. As a result, 31 more passed the second test than failed on it.What was the record of passing or failing on the first test? Please help with the equations & the solution. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218928 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=218928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = no. that originally passed<BR>\n" );
document.write( "Let y = no. that originally failed<BR>\n" );
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document.write( "\"In a business studies test, 30 more students passed than the number of those that failed.\"<BR>\n" );
document.write( "x - y = 30<BR>\n" );
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document.write( "\"In the next test, 7 students who passed the first test, failed & 1/3 of those who failed passed.\"<BR>\n" );
document.write( "(x-7) passed this test<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >y passed this test<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >y failed this time<BR>\n" );
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document.write( "\" As a result, 31 more passed the second test than failed on it.\"<BR>\n" );
document.write( "(x-7) - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >y = 31<BR>\n" );
document.write( "multiply by 3<BR>\n" );
document.write( "3(x-7) - 2y = 3(31)<BR>\n" );
document.write( "3x - 21 - 2y = 93<BR>\n" );
document.write( "3x - 2y = 93 + 21<BR>\n" );
document.write( "3x - 2y = 114<BR>\n" );
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document.write( "Use elimination on the 1st and 2nd test equations, multi the 1st eq by 2<BR>\n" );
document.write( "3x - 2y = 114<BR>\n" );
document.write( "2x - 2y = 60<BR>\n" );
document.write( "-----------------subtraction eliminates y, find x<BR>\n" );
document.write( "x = 54 originally passed<BR>\n" );
document.write( "Find y <BR>\n" );
document.write( "54 - y = 30<BR>\n" );
document.write( "54 - 30 = y<BR>\n" );
document.write( "y = 24 originally failed<BR>\n" );
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document.write( "Confirms these solutions in the statements:<BR>\n" );
document.write( "\" 7 students who passed the first test, failed & 1/3 of those who failed passed. <BR>\n" );
document.write( "As a result, 31 more passed the second test than failed on it.\"<BR>\n" );
document.write( "(54-7) - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(24) = <BR>\n" );
document.write( "47 - 16 = 31\r<BR>\n" );
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