document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=512744>Question 512744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two consecutive even integers such that the sum of the larger and 3 times the smaller is 234.<BR>\n" );
document.write( "As far as I got was x+3x=234 but then I got stuck and was not even sure that was right. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #342737 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=342737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's first think about consecutive even integers.  For example think of these consecutive even integers: 12, 14, 16, 18, 20 ... Notice that that there is a difference of 2 between consecutive even integers. Therefore, if X represents the smaller of two consecutive even integers, then the next even integer in the series would be represented as X + 2.<BR>\n" );
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document.write( "So, we can say that X represents the smaller integer in a series of even integers and X + 2 represents the next bigger even integer.<BR>\n" );
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document.write( "The problem tells you that the sum of the larger (X + 2) and 3 times the smaller (3 times X or just 3X) equals 234. So we can write the equation:<BR>\n" );
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document.write( "X + 2 + 3X = 234<BR>\n" );
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document.write( "Eliminate the 2 on the left side by subtracting 2 from BOTH sides. When you do the subtraction of 2 from BOTH the left and the right sides, the equation reduces to:<BR>\n" );
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document.write( "X + 3X = 232<BR>\n" );
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document.write( "Combine the X terms on the left side by adding them:<BR>\n" );
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document.write( "4X = 232<BR>\n" );
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document.write( "Solve for X by dividing BOTH sides by 4 to get:<BR>\n" );
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document.write( "X = 232/4 = 58<BR>\n" );
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document.write( "Since X = 58 and X represents the smaller of the 2 even numbers, the next larger consecutive even number is 60. The two consecutive even numbers you are looking for are 58 and 60.<BR>\n" );
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document.write( "Check by adding the larger (60) to 3 times the smaller (3*58). 3 times 58 is 174. Add 60 to 174 and you get 234. That checks out, so our answers 58 and 60 are correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. You were close with your equation, but you used X to represent both the smaller and the larger number. Your equation would have reduced to:<BR>\n" );
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document.write( "4X = 234<BR>\n" );
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document.write( "and when you divide both sides by 4 to solve for X, you would find that 4 does not divide evenly into 234. The answer would have been that X = 58 and a half and that would not be correct. The answer should be an integer (whole number).<BR>\n" );
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