document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=275440>Question 275440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two integers are 10.  Three times one integer is 3 less than 8 times the other integer. Find the numbers.\r<BR>\n" );
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document.write( "I have tried 3x + 8(10 - x) - 3=10, also 3(10 - x)+ 8x - 3, I've started out on x+y=10, so if one integer is x, the other has to be (10 - x), like x + (10 - x)=10, but no answer.  It seems like an easy one, can you help?\r<BR>\n" );
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document.write( "Thank you,\r<BR>\n" );
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document.write( "Alex Vargas<BR>\n" );
document.write( "avargas91702@hotmail.com </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854110 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13327)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have a problem common among students first learning to solve problems using algebra: turning the given information into a correct algebraic equation.<br><BR>\n" );
document.write( "You do, however, have a good start on another part of setting the problem up -- using the information that the sum of the two number is 10 to call the two numbers \"x\" and \"10-x\".<br><BR>\n" );
document.write( "Now for converting \"Three times one integer is 3 less than 8 times the other integer\" into a correct equation....<br><BR>\n" );
document.write( "\"Three times one integer...\"<BR>\n" );
document.write( "you have that part okay:<BR>\n" );
document.write( "Your equation to here is \"3x...\"<br><BR>\n" );
document.write( "\"... is\"<BR>\n" );
document.write( "That is your equals sign; think of it as saying \"is equal to\" instead of just \"is\"<BR>\n" );
document.write( "Now your equation is \"3x =...\"<br><BR>\n" );
document.write( "\"...3 less than 8 times the other integer\"<BR>\n" );
document.write( "Here is where beginning algebra students make a very common error.  They see the \"3 less...\" and they write \"3-...\".  But \"3 less than A\" is \"A - 3\", not \"3 - A\".  So<br><BR>\n" );
document.write( "\"x\" is your \"one number\", so the other number is \"10-x\".  Then \"8 times the other number\" is \"8(10-x)\", and finally \"3 less than 8 times the other number\" is \"8(10-x)-3\".<br><BR>\n" );
document.write( "And now you have the complete equation:<br><BR>\n" );
document.write( "\"3x = 8(10-x)-3\"<br><BR>\n" );
document.write( "Now you can solve using basic algebraic operations.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=8%2810-x%29-3 ALIGN=MIDDLE  ALT=\"3x=8%2810-x%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=80-8x-3 ALIGN=MIDDLE  ALT=\"3x=80-8x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=77-8x ALIGN=MIDDLE  ALT=\"3x=77-8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x=77 ALIGN=MIDDLE  ALT=\"11x=77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And the numbers are x=7 and (10-x)=3<br><BR>\n" );
document.write( "ANSWERS: 7 and 3<br><BR>\n" );
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