document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93017>Question 93017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the average (arithmetic mean) of x and y is k, which of the following is the average of x, y, and z?\r<BR>\n" );
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document.write( "(A) 2k + z/3<BR>\n" );
document.write( "(B) 2k +z/2<BR>\n" );
document.write( "(C) k+z/3<BR>\n" );
document.write( "(D) k+z/2<BR>\n" );
document.write( "(E) 2(k+z)/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67703 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=67703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> None of the given answers are correct.<BR>\n" );
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document.write( "Here's how you do the problem.<BR>\n" );
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document.write( "You are told that the average of x and y is equal to k. But how do you find the average<BR>\n" );
document.write( "of x and y? You add them together and divide by 2. So the average of x and y is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29%2F2 ALIGN=MIDDLE  ALT=\"%28x+%2B+y%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and setting that equal to k you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29%2F2+=+k ALIGN=MIDDLE  ALT=\"%28x+%2B+y%29%2F2+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the denominator by multiplying both sides of this equation by 2:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A%28x%2By%29%29%2F2+=+2k ALIGN=MIDDLE  ALT=\"%282%2A%28x%2By%29%29%2F2+=+2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel the two in the numerator and the two in the denominator on the left side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%282%29%2A%28x+%2B+y%29%29%2Fcross%282%29+=+2k ALIGN=MIDDLE  ALT=\"%28cross%282%29%2A%28x+%2B+y%29%29%2Fcross%282%29+=+2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and we end up with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+=+2k ALIGN=MIDDLE  ALT=\"+x+%2B+y+=+2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remember this result.<BR>\n" );
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document.write( "Now let's find the average (call it A) of x, y, and z. To average these three you add them<BR>\n" );
document.write( "together and divide by 3.  In equation form this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28x+%2B+y+%2B+z%29%2F3 ALIGN=MIDDLE  ALT=\"A+=+%28x+%2B+y+%2B+z%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29+=+2k ALIGN=MIDDLE  ALT=\"%28x+%2B+y%29+=+2k\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we can substitute 2k for x + y in the equation<BR>\n" );
document.write( "for A. When we make that substitution, the answer for A is given by the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%282k+%2B+z%29%2F3 ALIGN=MIDDLE  ALT=\"A+=+%282k+%2B+z%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The right side of this equation is the form of the answer. Notice that A equals a quantity<BR>\n" );
document.write( "that is divided by 3. So in your answer list you can eliminate answers B and D because <BR>\n" );
document.write( "they are divided by 2, not 3.<BR>\n" );
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document.write( "By the rules of algebraic combination for single line expressions, the other answers are:<BR>\n" );
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document.write( "(A) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k%2Bz%2F3 ALIGN=MIDDLE  ALT=\"2k%2Bz%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(C) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+%2B+z%2F3 ALIGN=MIDDLE  ALT=\"k+%2B+z%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(E) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28k+%2B+z%29%2F3 ALIGN=MIDDLE  ALT=\"2%2A%28k+%2B+z%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this multiplies out to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k+%2B+2z%29%2F3 ALIGN=MIDDLE  ALT=\"%282k+%2B+2z%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I suppose that (A) is supposed to be the correct answer, but it sure isn't written<BR>\n" );
document.write( "that way. The way it is written is:<BR>\n" );
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document.write( "(A) 2k + z/3<BR>\n" );
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document.write( "This actually translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k+%2B+z%2F3 ALIGN=MIDDLE  ALT=\"2k+%2B+z%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > because by the rules of algebraic combination<BR>\n" );
document.write( "you do the division first and then you do the addition.<BR>\n" );
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document.write( "Instead, it should have been written:<BR>\n" );
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document.write( "(A) (2k + x)/3<BR>\n" );
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document.write( "In this form you divide everything inside the parentheses by 3 which translates to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k+%2B+z%29%2F3 ALIGN=MIDDLE  ALT=\"%282k+%2B+z%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and this is the correct form of the answer.<BR>\n" );
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document.write( "Hope this clarifies the problem for you and helps you to see your way through it. </SPAN>\n" );
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