document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207220>Question 207220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need assistance with two separate word problems.\r<BR>\n" );
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document.write( "1) A car radiator contains 10 liters of a 30% solution. How many liters will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze?\r<BR>\n" );
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document.write( "2) You are planning to start a business that will require an investment of $90,000. You have found some people who are willing to share equally in the venture. If you find three more people, each person's share will decrease by $2500. how many people have you found so far?\r<BR>\n" );
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document.write( "Thank you immensely, \r<BR>\n" );
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document.write( "Andrew<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 #156755 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=156755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) A car radiator contains 10 liters of a 30% solution.<BR>\n" );
document.write( " How many liters will have to be replaced with pure antifreeze if the resulting<BR>\n" );
document.write( " solution is to be 50% antifreeze?<BR>\n" );
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document.write( "let x = amt of pure antifreeze to be added<BR>\n" );
document.write( "and also<BR>\n" );
document.write( "let x = amt of 30% solution to be removed<BR>\n" );
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document.write( ".30(10-x) + x = .50(10)<BR>\n" );
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document.write( "3 - .3x + x = 5<BR>\n" );
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document.write( "-.3x + 1x = 5 - 3<BR>\n" );
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document.write( ".7x = 2<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F.7 ALIGN=MIDDLE  ALT=\"2%2F.7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 2.857 liters of 30% solution replaced by pure antifreeze<BR>\n" );
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document.write( "Check solution:<BR>\n" );
document.write( ".30(10-2.857) + 2.857 = .50(10)<BR>\n" );
document.write( "2.143 + 2.857 = 5<BR>\n" );
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document.write( "2) You are planning to start a business that will require an investment of $90,000. <BR>\n" );
document.write( "You have found some people who are willing to share equally in the venture.<BR>\n" );
document.write( " If you find three more people, each person's share will decrease by $2500.<BR>\n" );
document.write( " how many people have you found so far?<BR>\n" );
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document.write( "Let x = no. of people so far:<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+3) = no. of people to decrease share by $2500<BR>\n" );
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document.write( "Original share amt = Three more share amt + $2500<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90000%2Fx ALIGN=MIDDLE  ALT=\"90000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90000%2F%28%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"90000%2F%28%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2500 <BR>\n" );
document.write( "Multiply equation x(x+3); results<BR>\n" );
document.write( "90000(x+3) = 90000x + 2500x(x+3)<BR>\n" );
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document.write( "90000x + 270000 = 90000x + 2500x^2 + 7500x<BR>\n" );
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document.write( "Arrange on the right:<BR>\n" );
document.write( "0 = 90000x - 90000x + 2500x^2 + 7500x - 270000<BR>\n" );
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document.write( "A quadratic equation:<BR>\n" );
document.write( "2500x^2 + 7500x - 270000 = 0<BR>\n" );
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document.write( "Simplify, divide by 2500<BR>\n" );
document.write( "x^2 + 3x - 108 = 0<BR>\n" );
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document.write( "Factors to:<BR>\n" );
document.write( "(x+12)(x-9) = 0<BR>\n" );
document.write( "Positive solution<BR>\n" );
document.write( "x = 9 people originally<BR>\n" );
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document.write( "Check solution:<BR>\n" );
document.write( "90000/9 = 10000<BR>\n" );
document.write( "90000/12 = 7500<BR>\n" );
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document.write( "difference 2500 </SPAN>\n" );
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