document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158188>Question 158188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm struggling on 2 algebra problems I have. If you could please help me I would greatly appreaciate it.\r<BR>\n" );
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document.write( "1)   The sum of two numbers is 43. One number plus three times the other number  is 65. What are the numbers?\r<BR>\n" );
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document.write( "  x + x = 43\r<BR>\n" );
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document.write( "  x + 3x = 65\r<BR>\n" );
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document.write( "2)   The difference between two numbers is 55. Four times the smaller number plus five times the larger number is 176. What are the numbers?\r<BR>\n" );
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document.write( "  z = smaller number \r<BR>\n" );
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document.write( "  y = larger number\r<BR>\n" );
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document.write( "  x - x = 55\r<BR>\n" );
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document.write( "  4z + 5y = 76\r<BR>\n" );
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document.write( "   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116560 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) The sum of two numbers is 43. One number plus three times the other number is 65. What are the numbers?<BR>\n" );
document.write( "x + x = 43<BR>\n" );
document.write( "x + 3x = 65<BR>\n" );
document.write( "You can't use the SAME variable to represent the two different numbers!  Use another variable:<BR>\n" );
document.write( "Let x = one number<BR>\n" );
document.write( "and y = second number<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x + y = 43 (equation 1)<BR>\n" );
document.write( "x + 3y = 65 (equation 2)<BR>\n" );
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document.write( "solve equation 1 for y:<BR>\n" );
document.write( "x + y = 43<BR>\n" );
document.write( "y = 43 - x<BR>\n" );
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document.write( "Substitute the above into equation 2 and solve for x:<BR>\n" );
document.write( "x + 3y = 65<BR>\n" );
document.write( "x + 3(43 - x) = 65<BR>\n" );
document.write( "x + 129 - 3x = 65<BR>\n" );
document.write( "129 - 2x = 65<BR>\n" );
document.write( "129 = 2x+65<BR>\n" );
document.write( "64 = 2x<BR>\n" );
document.write( "32 = x<BR>\n" );
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document.write( "Substitute the above into equation 1 and solve for y:<BR>\n" );
document.write( "x + y = 43<BR>\n" );
document.write( "32 + y = 43<BR>\n" );
document.write( "y = 11<BR>\n" );
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document.write( "Solution: the numbers are 11 and 32<BR>\n" );
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document.write( "2) The difference between two numbers is 55. Four times the smaller number plus five times the larger number is 176. What are the numbers?<BR>\n" );
document.write( "z = smaller number<BR>\n" );
document.write( "y = larger number<BR>\n" );
document.write( "x - x = 55   <<<<--how did you get x?  should be y-z=55<BR>\n" );
document.write( "4z + 5y = 76 <<<<--should be 176<BR>\n" );
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document.write( "Let's start over:<BR>\n" );
document.write( "z = smaller number<BR>\n" );
document.write( "y = larger number<BR>\n" );
document.write( "y - z = 55<BR>\n" );
document.write( "4z + 5y = 176<BR>\n" );
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document.write( "Solve equation 1 for y:<BR>\n" );
document.write( "y - z = 55<BR>\n" );
document.write( "y = z+55<BR>\n" );
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document.write( "Substitute the above into equation 2 and solve for z:<BR>\n" );
document.write( "4z + 5y = 176<BR>\n" );
document.write( "4z + 5(z+55) = 176<BR>\n" );
document.write( "4z + 5z + 275 = 176<BR>\n" );
document.write( "4z + 5z + 275 = 176<BR>\n" );
document.write( "9z + 275 = 176<BR>\n" );
document.write( "9z = -99<BR>\n" );
document.write( "z = -11<BR>\n" );
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document.write( "Substitute the above into equation 1 and solve for y:<BR>\n" );
document.write( "y - z = 55<BR>\n" );
document.write( "y - (-11) = 55<BR>\n" );
document.write( "y+11 = 55<BR>\n" );
document.write( "y = 44<BR>\n" );
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document.write( "Solution: the two numbers are -11 and 44 </SPAN>\n" );
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