document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133232>Question 133232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi would you please help me with this word problem?\r<BR>\n" );
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document.write( "A thief steals a number of plants from a nursery.  On the way out he encounters three security guards, one after another.  To each guard the thief is forced to give one half of the plants he still has plus two.  Finally the thief leaves the nursery with one lone plant—how many plants were originally stolen?\r<BR>\n" );
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document.write( "Let x/2+2 be the plants given to the first guard<BR>\n" );
document.write( "Let x/4+2 be the plants given to second guard<BR>\n" );
document.write( "Let x/8+2 be the plants given to third guard\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F2%2B2%29-%28x%2F4%2B2%29-%28x%2F8%2B2%29=1 ALIGN=MIDDLE  ALT=\"%28x%2F2%2B2%29-%28x%2F4%2B2%29-%28x%2F8%2B2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by LCD 8<BR>\n" );
document.write( "4x+16-2x-16-x-16=8<BR>\n" );
document.write( "x-16=8<BR>\n" );
document.write( "x=24\r<BR>\n" );
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document.write( "check: (12+2)-(6+2)-(3+2)=1  OK\r<BR>\n" );
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document.write( "	14+8+5+1= 28 plants stolen \r<BR>\n" );
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document.write( "But when you check the problem using 28 it does not work;\r<BR>\n" );
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document.write( ".5(28) +2 = 6, .5(16)+2=10, .5(10)+2= 7; 16+10+7=33+1=34 \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 #97436 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> GOOD!!!!!   YOU GAVE IT A SHOT<BR>\n" );
document.write( "WHEN THE GUARD GIVES, YOU NEED TO KEEP TRACK OF WHAT HE HAS LEFT.<BR>\n" );
document.write( "OK  I FIND IT EASIER TO WORK THESE WORD PROBLEMS IF I CLEARLY LAY OUT WHAT THE UNKNOWNS REPRESENT, SO:\r<BR>\n" );
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document.write( "Let x= the number of plants originally stolen\r<BR>\n" );
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document.write( "The thief gives (x/2)+2 plants to the first guard<BR>\n" );
document.write( "Thief then has x-((x/2)+2) or 2x/2-(x/2)-2 =(x/2)-2 plants left<BR>\n" );
document.write( "Thief gives 1/2((x/2-2)+2) or (x/4)-1+2=(x/4)+1 to second guard\r<BR>\n" );
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document.write( "Thief then has ((x/2)-2)-((x/4)+1) or (x/2)-2-(x/4)-1=(x/4)-3 plants left\r<BR>\n" );
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document.write( "Thief gives 1/2((x/4)-3)+2 or (x/8)-(3/2)+2=(x/8)+1/2 to third guard<BR>\n" );
document.write( "Thief has left ((x/4)-3)-((x/8)+1/2) and we are told that this equals 1, so:\r<BR>\n" );
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document.write( "(x/4)-3-(x/8)-1/2=1  multiply each term by 8\r<BR>\n" );
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document.write( "2x-24-x-4=8 simplify<BR>\n" );
document.write( "x-28=8  add 28 to both sides\r<BR>\n" );
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document.write( "x-28+28=8+28<BR>\n" );
document.write( "x=36-----------------number of pLAnts originally stolen\r<BR>\n" );
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document.write( "Ck<BR>\n" );
document.write( "First guard<BR>\n" );
document.write( "Gives 1/2(36)+2=18+2=20<BR>\n" );
document.write( "Has left 36-20=16<BR>\n" );
document.write( "Second guard<BR>\n" );
document.write( "Gives 1/2(16)+2=10<BR>\n" );
document.write( "Has left 16-10=6\r<BR>\n" );
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document.write( "Third guard<BR>\n" );
document.write( "Gives 1/2(6)+2=5<BR>\n" );
document.write( "Has left 6-5=1 \r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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