document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388997>Question 388997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 27. One half of the first number plus one third of the second number is 11. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275461 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><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=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a+b=27_(1)/(2)*a+(1)/(3)*b=11\r<BR>\n" );
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document.write( "Multiply (1)/(2) by a to get (a)/(2).<BR>\n" );
document.write( "a+b=27_(a)/(2)+(1)/(3)*b=11\r<BR>\n" );
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document.write( "Multiply (1)/(3) by b to get (b)/(3).<BR>\n" );
document.write( "a+b=27_(a)/(2)+(b)/(3)=11\r<BR>\n" );
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document.write( "Since b does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting b from both sides.<BR>\n" );
document.write( "a=-b+27_(a)/(2)+(b)/(3)=11\r<BR>\n" );
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document.write( "Replace all occurrences of a with the solution found by solving the last equation for a.  In this case, the value substituted is -b+27.<BR>\n" );
document.write( "a=-b+27_(-b+27)/(2)+(b)/(3)=11\r<BR>\n" );
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document.write( "Remove the parentheses around the expression -b+27.<BR>\n" );
document.write( "a=-b+27_(-b+27)/(2)+(b)/(3)=11\r<BR>\n" );
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document.write( "Divide each term in the numerator by the denominator.<BR>\n" );
document.write( "a=-b+27_-(b)/(2)+(27)/(2)+(b)/(3)=11\r<BR>\n" );
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document.write( "Combine the numerators of all expressions that have common denominators.<BR>\n" );
document.write( "a=-b+27_(-b+27)/(2)+(b)/(3)=11\r<BR>\n" );
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document.write( "Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of 6. The ((-b+27))/(2) expression needs to be multiplied by ((3))/((3)) to make the denominator 6. The (b)/(3) expression needs to be multiplied by ((2))/((2)) to make the denominator 6.<BR>\n" );
document.write( "a=-b+27_(-b+27)/(2)*(3)/(3)+(b)/(3)*(2)/(2)=11\r<BR>\n" );
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document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6.<BR>\n" );
document.write( "a=-b+27_((-b+27)(3))/(6)+(b)/(3)*(2)/(2)=11\r<BR>\n" );
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document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6.<BR>\n" );
document.write( "a=-b+27_((-b+27)(3))/(6)+(b(2))/(6)=11\r<BR>\n" );
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document.write( "The numerators of expressions that have equal denominators can be combined.  In this case, ((-b+27)(3))/(6) and ((b(2)))/(6) have the same denominator of 6, so the numerators can be combined.<BR>\n" );
document.write( "a=-b+27_((-b+27)(3)+(b(2)))/(6)=11\r<BR>\n" );
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document.write( "Simplify the numerator of the expression.<BR>\n" );
document.write( "a=-b+27_(-b+81)/(6)=11\r<BR>\n" );
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document.write( "Multiply each term in the equation by 6.<BR>\n" );
document.write( "a=-b+27_(-b+81)/(6)*6=11*6\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "a=-b+27_-b+81=11*6\r<BR>\n" );
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document.write( "Multiply 11 by 6 to get 66.<BR>\n" );
document.write( "a=-b+27_-b+81=66\r<BR>\n" );
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document.write( "Since 81 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 81 from both sides.<BR>\n" );
document.write( "a=-b+27_-b=-81+66\r<BR>\n" );
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document.write( "Add 66 to -81 to get -15.<BR>\n" );
document.write( "a=-b+27_-b=-15\r<BR>\n" );
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document.write( "Multiply each term in the equation by -1.<BR>\n" );
document.write( "a=-b+27_-b*-1=-15*-1\r<BR>\n" );
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document.write( "Multiply -b by -1 to get b.<BR>\n" );
document.write( "a=-b+27_b=-15*-1\r<BR>\n" );
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document.write( "Multiply -15 by -1 to get 15.<BR>\n" );
document.write( "a=-b+27_b=15\r<BR>\n" );
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document.write( "Replace all occurrences of b with the solution found by solving the last equation for b.  In this case, the value substituted is 15.<BR>\n" );
document.write( "a=-(15)+27_b=15\r<BR>\n" );
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document.write( "Multiply -1 by the 15 inside the parentheses.<BR>\n" );
document.write( "a=-15+27_b=15\r<BR>\n" );
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document.write( "Add 27 to -15 to get 12.<BR>\n" );
document.write( "a=12_b=15\r<BR>\n" );
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document.write( "This is the solution to the system of equations.<BR>\n" );
document.write( "a=12_b=15 </SPAN>\n" );
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