document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201030>Question 1201030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of 1000 adults aged 18 and older, the following question was posed:<BR>\n" );
document.write( "\"Are other travelers' online reviews trustworthy?\" The participants were asked<BR>\n" );
document.write( "to answer \"yes,\" \"no,\" or \"not sure.\" The survey revealed that 340 answered \"no\"<BR>\n" );
document.write( "or \"not sure.\" It also showed that the number of those who answered \"yes\"<BR>\n" );
document.write( "exceeded the number of those who answered \"no\" by 400. What percentage of<BR>\n" );
document.write( "respondents answered \"yes,\" \"no,\" and \"not sure\"? (Let x represent the number of<BR>\n" );
document.write( "respondents who answered \"yes\", y represent the number of respondents who<BR>\n" );
document.write( "answered \"no\", and z represent the number of respondents who answered \"not<BR>\n" );
document.write( "sure\".)<BR>\n" );
document.write( " 	? = 	1000<BR>\n" );
document.write( " 	? = 	340<BR>\n" );
document.write( " 	?  = 	400\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835299 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=835299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Building from what the tutor Edwin McCravy mentioned<BR>\n" );
document.write( "x + y+z = 1000<BR>\n" );
document.write( "x + <font color=red>y+z</font> = 1000<BR>\n" );
document.write( "x + <font color=red>340</font> = 1000\r<BR>\n" );
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document.write( "This replacement, aka substitution, is valid because y+z = 340 was the second equation he formed.\r<BR>\n" );
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document.write( "Solving for x:<BR>\n" );
document.write( "x+340 = 1000<BR>\n" );
document.write( "x = 1000-340<BR>\n" );
document.write( "x = 660<BR>\n" );
document.write( "There were 660 people who responded \"yes\" (they find online travel reviews trustworthy).\r<BR>\n" );
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document.write( "We can then plug this into the third equation he formed to find y.<BR>\n" );
document.write( "x-y = 400 <BR>\n" );
document.write( "660-y = 400 <BR>\n" );
document.write( "-y = 400-660<BR>\n" );
document.write( "-y = -260<BR>\n" );
document.write( "y = 260<BR>\n" );
document.write( "There were 260 people who responded \"no\" (they don't find online travel reviews trustworthy).\r<BR>\n" );
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document.write( "Use that value of y to determine z.<BR>\n" );
document.write( "y+z = 340<BR>\n" );
document.write( "260+z = 340<BR>\n" );
document.write( "z = 340-260<BR>\n" );
document.write( "z = 80<BR>\n" );
document.write( "There were 80 people who weren't sure if the online travel reviews were trustworthy or not.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "x+y+z = 1000<BR>\n" );
document.write( "660+260+80 = 1000<BR>\n" );
document.write( "1000 = 1000 ..... 1st equation works<BR>\n" );
document.write( "and<BR>\n" );
document.write( "y+z = 340<BR>\n" );
document.write( "260+80 = 340<BR>\n" );
document.write( "340 = 340 ....... 2nd equation works<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x-y = 400<BR>\n" );
document.write( "660-260 = 400<BR>\n" );
document.write( "400 = 400 ...... 3rd equation works<BR>\n" );
document.write( "All three original equations are true for (x,y,z) = (660,260,80) <BR>\n" );
document.write( "Those values are fully confirmed.\r<BR>\n" );
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document.write( "Now to compute percentages, we divide each by 1000<BR>\n" );
document.write( "x = 660 leads to x/1000 = 660/1000 = 0.66 = 66%<BR>\n" );
document.write( "Therefore, 66% of the participants said \"yes\".<BR>\n" );
document.write( "y = 260 leads to y/1000 = 260/1000 = 0.26 = 26%<BR>\n" );
document.write( "26% of the participants said \"no\".<BR>\n" );
document.write( "z = 80 leads to z/1000 = 80/1000 = 0.08 = 8%<BR>\n" );
document.write( "8% of the participants said \"not sure\".\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "x = 660 ----> 66% said \"yes\"<BR>\n" );
document.write( "y = 260 ----> 26% said \"no\"<BR>\n" );
document.write( "z = 80 -----> 8% said \"not sure\"<BR>\n" );
document.write( "Note the percentages add to 100 percent ( 66+26+8 = 100)<BR>\n" );
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