document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76284>Question 76284</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I know I could get one question like this if someone could explain it to me - Three times the smaller of 2 numbers increased by 5 times the larger is 229. Four times the smaller decreased by 25 equals 3 times the larger. Find the numbers.<BR>\n" );
document.write( "I started out with - x=bigger number, and y=smaller number<BR>\n" );
document.write( "3y+5x=229 (first equation)<BR>\n" );
document.write( "4y-25=3x (second equation)<BR>\n" );
document.write( "How do you go on? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54744 by </B><A HREF=/tutors/aboutme.mpl?userid=wodkit02><B>wodkit02(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=wodkit02><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Once you have 2 simultaneous equations, you can solve for a variable in one equation by using a modified version of the other.\r<BR>\n" );
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document.write( "For this particular question, your equations are correct. So we have <BR>\n" );
document.write( "3y+5x=229<BR>\n" );
document.write( "4y-25=3x\r<BR>\n" );
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document.write( "I'm going to start by putting the 2nd equation in terms of x, so when I solve for x I get:<BR>\n" );
document.write( "4y-25=3x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y-25%29%2F3 ALIGN=MIDDLE  ALT=\"%284y-25%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=x (I divided each side by 3)\r<BR>\n" );
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document.write( "Now I can plug in that x value into the 1st equation, so I can solve for y.<BR>\n" );
document.write( "3y+5x=229<BR>\n" );
document.write( "3y+5*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284y-25%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28%284y-25%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=229....distribute the 5 to everything in the parenthesis to get<BR>\n" );
document.write( "3y+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820y-125%29%2F3 ALIGN=MIDDLE  ALT=\"%2820y-125%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=229....now convert each term on the left side into like fractions of denominator 3 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289y%2F3%29 ALIGN=MIDDLE  ALT=\"%289y%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820y-125%29%2F3 ALIGN=MIDDLE  ALT=\"%2820y-125%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=229....now multiply each side by 3 to get rid of the fraction to get<BR>\n" );
document.write( "9y+20y-125=687...add like terms to get<BR>\n" );
document.write( "29y-125=687...add 125 to each side to get<BR>\n" );
document.write( "29y=812...finally, we can divide to get<BR>\n" );
document.write( "y=28\r<BR>\n" );
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document.write( "Back to the 2nd equation, we can now plug in a number for y, and then solve for x:<BR>\n" );
document.write( "4y-25=3x<BR>\n" );
document.write( "4(28)-25=3x<BR>\n" );
document.write( "112-25=3x<BR>\n" );
document.write( "87=3x<BR>\n" );
document.write( "29=x\r<BR>\n" );
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document.write( "So the numbers are 28 and 29.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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