document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78145>Question 78145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One number is 3 more than 2 times the other, and their sum is 27. what are 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 #56041 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=56041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The hardest part of this problem is translating the words into equations.<BR>\n" );
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document.write( "The problem uses the words \"one number\" and \"the other\". This tells you that there are two<BR>\n" );
document.write( "numbers to be found.  Call \"one number\" x and \"the other\" y.<BR>\n" );
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document.write( "The first sentence tells you that \"one number\" (the one we called x) is 3 more than twice<BR>\n" );
document.write( "\"the other\" and we called that y.  Twice y is 2y and 3 more than that is 2y + 3.<BR>\n" );
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document.write( "So from the first sentence we know that x = 2y + 3.<BR>\n" );
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document.write( "The first sentence also tells us that when we add \"one number\" to \"the other\" the sum is<BR>\n" );
document.write( "27.  In equation form this is x + y = 27.<BR>\n" );
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document.write( "Now we have two equations as follows:<BR>\n" );
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document.write( "x = 2y + 3 and<BR>\n" );
document.write( "x + y = 27 <BR>\n" );
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document.write( "Since we have two unknowns (x and y) we must have two equations to solve for the two unknowns,<BR>\n" );
document.write( "and we have our two equations.<BR>\n" );
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document.write( "One of the ways to solve these two is by substitution.  Notice that the first equation<BR>\n" );
document.write( "tells us that x is equal to the right side and the right side has only one unknown, y.<BR>\n" );
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document.write( "So we can take the right side of the first equation and plug it into the second equation<BR>\n" );
document.write( "in place of x.  When we do that we get:<BR>\n" );
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document.write( "(2y + 3) + y = 27<BR>\n" );
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document.write( "The parentheses are just there to show you that we replaced the x that was there with 2y + 3.<BR>\n" );
document.write( "We can remove the parentheses to make the equation:<BR>\n" );
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document.write( "2y + 3 + y = 27<BR>\n" );
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document.write( "Add the terms containing y and the equation becomes:<BR>\n" );
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document.write( "3y + 3 = 27<BR>\n" );
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document.write( "We need to eliminate the + 3 on the left side.  We can do that by subtracting 3 from the<BR>\n" );
document.write( "left side, but if we do that we must also subtract 3 from the right side to keep the equation<BR>\n" );
document.write( "in balance.  This subtraction results in:<BR>\n" );
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document.write( "3y + 3 - 3 = 27 - 3<BR>\n" );
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document.write( "and this simplifies to:<BR>\n" );
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document.write( "3y = 24<BR>\n" );
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document.write( "Now you can solve for y by dividing both sides by 3 to get:<BR>\n" );
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document.write( "3y/3 = 24/3<BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "y = 8<BR>\n" );
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document.write( "We now know one of the unknowns.  Recall that one of our equations said that the sum of the<BR>\n" );
document.write( "two unknowns must be 27. In equation form we wrote the equation:<BR>\n" );
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document.write( "x + y = 27<BR>\n" );
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document.write( "But we know that y is 8. So in this equation we can replace y by 8 and get:<BR>\n" );
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document.write( "x + 8 = 27<BR>\n" );
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document.write( "We can solve for this by subtracting 8 from both sides of the equation to get:<BR>\n" );
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document.write( "x = 27 - 8 = 19<BR>\n" );
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document.write( "In summary, we have found that the two unknowns are 19 and 8.<BR>\n" );
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document.write( "Check ... does their sum equal 27? Yes it does. And is 19 equal to twice 8 = 3? Well, twice<BR>\n" );
document.write( "8 is 16 and add 3 gives you 19 ... so this condition was met by the two numbers also.<BR>\n" );
document.write( "We have found an answer using the process of substitution and have checked our answer.<BR>\n" );
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document.write( "Hope this discussion helps you to see a way to work problems by substitution.<BR>\n" );
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