document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097569>Question 1097569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chemical manufacturer wishes to fill an order for 700 gallons of a 24% acid solution. Solutions of 20% and 30% are in stock. How many gallons of 30% acid solution will be used in the desired mixture?\r<BR>\n" );
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document.write( "(I understand there may not be such a thing as \"24% acid solution\", et cetera. I'm just focusing on what solution needs to be used to get the number being asked for.<BR>\n" );
document.write( "Honestly, I've seen problems like these before but just have trouble when it's worded differently. Thank you!) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712011 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=712011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "\"A chemical manufacturer wishes to fill an order for 700 gallons of a 24% acid solution\" means they want 700*0.24 = 168 gallons of pure acid\r<BR>\n" );
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document.write( "Let <BR>\n" );
document.write( "x = amount of the 20% acid solution<BR>\n" );
document.write( "y = amount of the 30% acid solution<BR>\n" );
document.write( "both amounts are in gallons\r<BR>\n" );
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document.write( "Since we can only use the 20% or the 30% solution, this means that x and y must add to the total of 700\r<BR>\n" );
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document.write( "So we have the equation<BR>\n" );
document.write( "x+y = 700\r<BR>\n" );
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document.write( "Now solve for y. Subtract x from both sides<BR>\n" );
document.write( "x+y = 700<BR>\n" );
document.write( "x+y-x = 700-x<BR>\n" );
document.write( "y = 700-x<BR>\n" );
document.write( "Keep this equation in mind. We'll use this equation later\r<BR>\n" );
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document.write( "If we use x gallons of the 20% solution, then we have 0.20*x gallons of pure acid. If we use y gallons of the 30% solution, then we have 0.30*y gallons of pure acid. Combined we have 0.20*x+0.30*y gallons of pure acid. Recall that above we want the target amouunt of total pure acid to be 168 gallons. That is how we're able to get the equation below\r<BR>\n" );
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document.write( "0.20*x + 0.30*y = 168\r<BR>\n" );
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document.write( "Now use the equation y = 700-x to perform substitution<BR>\n" );
document.write( "0.20*x + 0.30*y = 168<BR>\n" );
document.write( "0.20*x + 0.30*( y ) = 168<BR>\n" );
document.write( "0.20*x + 0.30*( 700 - x ) = 168 ... y has been replaced with 700-x\r<BR>\n" );
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document.write( "With y gone from the equation, we can now solve for x<BR>\n" );
document.write( "0.20*x + 0.30*( 700 - x ) = 168<BR>\n" );
document.write( "0.20*x + 0.30*( 700 ) + 0.30*( - x ) = 168<BR>\n" );
document.write( "0.20*x + 210 - 0.30x = 168<BR>\n" );
document.write( "0.20x - 0.30x + 210 = 168<BR>\n" );
document.write( "-0.10x + 210 = 168<BR>\n" );
document.write( "-0.10x + 210-210 = 168-210<BR>\n" );
document.write( "-0.10x = -42<BR>\n" );
document.write( "-0.10x/(-0.10) = -42/(-0.10)<BR>\n" );
document.write( "x = 420\r<BR>\n" );
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document.write( "Use this x value to find y (again use y = 700-x)<BR>\n" );
document.write( "y = 700-x<BR>\n" );
document.write( "y = 700-420 ... replace x with 420<BR>\n" );
document.write( "y = 280\r<BR>\n" );
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document.write( "----------------------------------------------------\r<BR>\n" );
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document.write( "In summary we found that <BR>\n" );
document.write( "<font color=red>x = 420</font><BR>\n" );
document.write( "<font color=blue>y = 280</font>\r<BR>\n" );
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document.write( "So we should use <font color=red>420 gallons</font> of the 20% solution, and <font color=blue>280 gallons</font> of the 30% solution.<BR>\n" );
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