document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=968847>Question 968847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One number is bigger than another number. When one third of smaller number is taken away from a half of the bigger number the answer is 10. What is the smaller number?\r<BR>\n" );
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document.write( "How do you do it ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591971 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are an infinite number of values that satisfy this problem statement.\r<BR>\n" );
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document.write( "the problem statement is:\r<BR>\n" );
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document.write( "one number is bigger than another number.\r<BR>\n" );
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document.write( "1/2 * the bigger number minus 1/3 * the smaller number is equal to 10.\r<BR>\n" );
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document.write( "let y be the bigger number.\r<BR>\n" );
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document.write( "let x be the smaller number.\r<BR>\n" );
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document.write( "1/2 * y - 1/3 * x = 10\r<BR>\n" );
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document.write( "solve for y to get y = 20 + 2/3 * x.\r<BR>\n" );
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document.write( "that's the first equation.\r<BR>\n" );
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document.write( "the second equation that has to be satisfied is y > x.\r<BR>\n" );
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document.write( "so, what is happening is that y has to be equal to 20 + 2/3 * x and y has to be greater than x at the same time.\r<BR>\n" );
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document.write( "these two equations have to be solved simultaneously.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "y = 20 + 2/3 * x<BR>\n" );
document.write( "y > x\r<BR>\n" );
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document.write( "since y = 20 + 2/3 * x, the second equation can replace y with 20 + 2/3 * x to get:\r<BR>\n" );
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document.write( "20 + 2/3 * x > x\r<BR>\n" );
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document.write( "subtract 2/3 * x from both sides of this equation to get:\r<BR>\n" );
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document.write( "20 > x - 2/3 * x which becomes:\r<BR>\n" );
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document.write( "20 > 1/3 * x\r<BR>\n" );
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document.write( "multiply both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "60 > x\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "x has to be smaller than 60 and y has to be equal to 20 + 2/3 * x.\r<BR>\n" );
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document.write( "the problem statement will be satisfied when those two events occur.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "let x = 30.\r<BR>\n" );
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document.write( "when x = 30, y has to be equal to 20 + 2/3 * 30 = 20 + 20 = 40.\r<BR>\n" );
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document.write( "you have = 30 and y = 40\r<BR>\n" );
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document.write( "y is the bigger number.\r<BR>\n" );
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document.write( "1/2 * y - 1/3 * x must be equal to 10.\r<BR>\n" );
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document.write( "1/2 * 40 - 1/3 * 30 = 20 - 10 = 10\r<BR>\n" );
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document.write( "both equations have been satisfied.\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "y = 20 + 3/2 * x and x < 60.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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