document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=723929>Question 723929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a typical group of 1000 workers from each of the boatbuilding, iron foundry, and amusement park/arcade industries, there were 30 more injuries in iron foundries (I) than in amusement parks/arcades (A). There were 12 more injuries in amusement parks/arcades than in boatbuildings (B). Among these workers, there were 387 nonfatal occupational injuries. How many injuries took place in each industry?\r<BR>\n" );
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document.write( "I'm guessing (keyword being guessing) that:<BR>\n" );
document.write( "Data:1000 workers, I had 30 more than A and A had 12 more than B and the total is 387.<BR>\n" );
document.write( "Variable: A= amusement parks/arcades, B= boatbuildings, I= iron foundry<BR>\n" );
document.write( "Plan: B+(B+A)+(B+I)= 387<BR>\n" );
document.write( "Equation: B+(B+12)+(B+30)=387<BR>\n" );
document.write( "          3B+42 = 387<BR>\n" );
document.write( "            -42   -42<BR>\n" );
document.write( "             3B = 345<BR>\n" );
document.write( "           3B/3   345/3<BR>\n" );
document.write( "             B = 115<BR>\n" );
document.write( "Solution: A= 127, B= 115, and I= 145<BR>\n" );
document.write( "Am I right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443474 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "there were <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=387 ALIGN=MIDDLE  ALT=\"387\"   DISABLED_style= \"max-width:90%; height:auto;\" > nonfatal occupational injuries\r<BR>\n" );
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document.write( "let the boat-building injuries be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >,amusement park/arcade injuries be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and iron foundry injuries be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I ALIGN=MIDDLE  ALT=\"I\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2BA%2BI=387 ALIGN=MIDDLE  ALT=\"B%2BA%2BI=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=B%2B12 ALIGN=MIDDLE  ALT=\"A=B%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=A%2B30 ALIGN=MIDDLE  ALT=\"I=A%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >...substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=B%2B12%2B30 ALIGN=MIDDLE  ALT=\"I=B%2B12%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=B%2B42 ALIGN=MIDDLE  ALT=\"I=B%2B42\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2BA%2BI=387 ALIGN=MIDDLE  ALT=\"B%2BA%2BI=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >...plug in all values\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2B%28B%2B12%29%2B%28B%2B42%29=387 ALIGN=MIDDLE  ALT=\"B%2B%28B%2B12%29%2B%28B%2B42%29=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3B%2B12%2B42=387 ALIGN=MIDDLE  ALT=\"3B%2B12%2B42=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3B%2B54=387 ALIGN=MIDDLE  ALT=\"3B%2B54=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3B=387-54 ALIGN=MIDDLE  ALT=\"3B=387-54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3B=333 ALIGN=MIDDLE  ALT=\"3B=333\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=333%2F3 ALIGN=MIDDLE  ALT=\"B=333%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=111%29 ALIGN=MIDDLE  ALT=\"highlight%28B=111%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I ALIGN=MIDDLE  ALT=\"I\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=B%2B12 ALIGN=MIDDLE  ALT=\"A=B%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=111%2B12 ALIGN=MIDDLE  ALT=\"A=111%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=123%29 ALIGN=MIDDLE  ALT=\"highlight%28A=123%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=B%2B42 ALIGN=MIDDLE  ALT=\"I=B%2B42\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=111%2B42 ALIGN=MIDDLE  ALT=\"I=111%2B42\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28I=153%29 ALIGN=MIDDLE  ALT=\"highlight%28I=153%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check their sum:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2BA%2BI=387 ALIGN=MIDDLE  ALT=\"B%2BA%2BI=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=111%2B123%2B153=387 ALIGN=MIDDLE  ALT=\"111%2B123%2B153=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=387=387 ALIGN=MIDDLE  ALT=\"387=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check your solution: A= 127, B= 115, and I= 145<BR>\n" );
document.write( "Am I right?\r<BR>\n" );
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document.write( "your equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2B%28B%2B12%29%2B%28B%2B30%29=387 ALIGN=MIDDLE  ALT=\"B%2B%28B%2B12%29%2B%28B%2B30%29=387\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...you put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=%28B%2B30%29 ALIGN=MIDDLE  ALT=\"I=%28B%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but it is given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I ALIGN=MIDDLE  ALT=\"I\"   DISABLED_style= \"max-width:90%; height:auto;\" > had <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=A%2B30 ALIGN=MIDDLE  ALT=\"I=A%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you need to put <BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2BA%2B%28A%2B30%29=387 ALIGN=MIDDLE  ALT=\"B%2BA%2B%28A%2B30%29=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "since also given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > had <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=B%2B12 ALIGN=MIDDLE  ALT=\"A=B%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we go back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I ALIGN=MIDDLE  ALT=\"I\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=A%2B30 ALIGN=MIDDLE  ALT=\"I=A%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=B%2B12%2B30=B%2B42 ALIGN=MIDDLE  ALT=\"I=B%2B12%2B30=B%2B42\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now, plug it in equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2B%28B%2B12%29%2B%28B%2B42%29=387 ALIGN=MIDDLE  ALT=\"B%2B%28B%2B12%29%2B%28B%2B42%29=387\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );