document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=330156>Question 330156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) the greater of two numbers is 12 more than the smaller and the sum of the two numbers is 10 find the numbers<BR>\n" );
document.write( "2) one number is 5 times another if 18 is subtracted from the greater the remainder will be 3 times the smaller find the numbers<BR>\n" );
document.write( "3) divide 534 into three parts such that the second part will be 32 less than twice the first and the third will be 18 more than the first.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #236602 by </B><A HREF=/tutors/aboutme.mpl?userid=privani><B>privani(34)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=privani><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=236602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) the greater of two numbers is 12 more than the smaller and the sum of the two numbers is 10 find the numbers\r<BR>\n" );
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document.write( "Let's say the greater number=A, the smaller number=a.<BR>\n" );
document.write( "Form equations:<BR>\n" );
document.write( "A = a + 12.... (1)<BR>\n" );
document.write( "A + a = 10.... (2)\r<BR>\n" );
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document.write( "Substitute (1) in (2):<BR>\n" );
document.write( "A + a = 10<BR>\n" );
document.write( "(a + 12) + a = 10<BR>\n" );
document.write( "a + 12 + a = 10<BR>\n" );
document.write( "12 + 2a = 10<BR>\n" );
document.write( "2a = 10 - 12<BR>\n" );
document.write( "a = -2/2<BR>\n" );
document.write( "a = -1.... (3)\r<BR>\n" );
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document.write( "Substitute (3) in (1)<BR>\n" );
document.write( "A = a + 12<BR>\n" );
document.write( "A = -1 + 12<BR>\n" );
document.write( "A = 11\r<BR>\n" );
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document.write( "Therefore, the greater number is 11 and the smaller number is -1.\r<BR>\n" );
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document.write( "2) one number is 5 times another if 18 is subtracted from the greater the remainder will be 3 times the smaller find the numbers<BR>\n" );
document.write( "Assuming: \"One number is 5 times another. If 18 is subtracted from the greater, the remainder will be 3 times the smaller. Find the numbers.\"\r<BR>\n" );
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document.write( "Assume: X = the greater number, x =  the smaller number\r<BR>\n" );
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document.write( "Form equations:<BR>\n" );
document.write( "N=5n   .... (1)<BR>\n" );
document.write( "N-18=3n.... (2)\r<BR>\n" );
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document.write( "Substitute (1) in (2)<BR>\n" );
document.write( "N-18=3n<BR>\n" );
document.write( "5n-18=3n<BR>\n" );
document.write( "5n-3n=18<BR>\n" );
document.write( "2n=18<BR>\n" );
document.write( "n=18/2<BR>\n" );
document.write( "n=9\r<BR>\n" );
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document.write( "Substitute n=9 in (1)<BR>\n" );
document.write( "N=5n<BR>\n" );
document.write( "N=5*9<BR>\n" );
document.write( "N=45\r<BR>\n" );
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document.write( "Therefore, the greater number is 45 and the smaller number is 9.\r<BR>\n" );
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document.write( "3) divide 534 into three parts such that the second part will be 32 less than twice the first and the third will be 18 more than the first.\r<BR>\n" );
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document.write( "Assume: first part=a, second part=b, third part=c<BR>\n" );
document.write( "Form equations:<BR>\n" );
document.write( "a+b+c=534....(1)<BR>\n" );
document.write( "b-32=2a<BR>\n" );
document.write( "b=2a+32....(2)<BR>\n" );
document.write( "c+18=a....(3)\r<BR>\n" );
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document.write( "Substitute (3) in (2)<BR>\n" );
document.write( "b=2a+32<BR>\n" );
document.write( "b=2(c+18)+32<BR>\n" );
document.write( "b=2c+36+32<BR>\n" );
document.write( "b=2c+68....(4)\r<BR>\n" );
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document.write( "Substitute (3) and (4) in (1)<BR>\n" );
document.write( "a+b+c=534<BR>\n" );
document.write( "(c+18)+(2c+68)+c=534<BR>\n" );
document.write( "c+18+2c+68+c=534<BR>\n" );
document.write( "4c+86=534<BR>\n" );
document.write( "4c=534-86<BR>\n" );
document.write( "c=448/4<BR>\n" );
document.write( "c=112\r<BR>\n" );
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document.write( "Substitute c=112 in (4)<BR>\n" );
document.write( "b=2c+68<BR>\n" );
document.write( "b=2(112)+68<BR>\n" );
document.write( "b=224+68<BR>\n" );
document.write( "b=292\r<BR>\n" );
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document.write( "Substitute c=112, b=292 in (1)<BR>\n" );
document.write( "a+b+c=534<BR>\n" );
document.write( "a+292+112=534<BR>\n" );
document.write( "a=534-292-112<BR>\n" );
document.write( "a=130\r<BR>\n" );
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document.write( "So, the first part=130, the second part=292 and the third part=112. </SPAN>\n" );
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