document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619474>Question 619474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was given a practice test and I missed a section in class. I know the answer to the word problems below.. but I am not sure how to set up the equations to get the correct answers. There are 2 questions below:\r<BR>\n" );
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document.write( "1-A lab has a 10% acid solution and a 25% acid solution. How many liters of each are required to get 300L of a 15% acid solution?\r<BR>\n" );
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document.write( "Answer: 200 at 10%<BR>\n" );
document.write( "        100 at 25%\r<BR>\n" );
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document.write( "BUT HOW?!?!\r<BR>\n" );
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document.write( "2-Two trains leave Chicago at the same time and in opposite directions. One is going 120MPH and one is going 130MPH. How long before they are 750 miles apart?\r<BR>\n" );
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document.write( "Answer: 6 \r<BR>\n" );
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document.write( "once again.. HOW?!\r<BR>\n" );
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document.write( "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 #389671 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=389671\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started. Post the other question if you still need help with it.\r<BR>\n" );
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document.write( "# 1\r<BR>\n" );
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document.write( "Let x = amount of 10% solution and y = amount of 25% solution\r<BR>\n" );
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document.write( "We want our final solution to be 300 L, so x+y = 300. Solve this for y to get y = 300 - x\r<BR>\n" );
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document.write( "Since you have x liters of the 10% solution, you have exactly 0.1x liters of acid. Similarly, since you have y liters of the 25% solution, you have exactly 0.25y liters of acid\r<BR>\n" );
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document.write( "In total, you have 0.1x+0.25y liters of pure acid. We want our final solution to be 15% acid, so there must be 300*0.15 = 45 liters of pure acid in the final solution (mixed with water and other chemicals)\r<BR>\n" );
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document.write( "So we can say 0.1x+0.25y = 45\r<BR>\n" );
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document.write( "0.1x+0.25y = 45\r<BR>\n" );
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document.write( "0.1x+0.25(300 - x) = 45\r<BR>\n" );
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document.write( "0.1x+0.25(300) - 0.25x = 45\r<BR>\n" );
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document.write( "0.1x + 75 - 0.25x = 45\r<BR>\n" );
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document.write( "-0.15x + 75 = 45\r<BR>\n" );
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document.write( "-0.15x = 45 - 75\r<BR>\n" );
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document.write( "-0.15x = -30\r<BR>\n" );
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document.write( "x = -30/(-0.15)\r<BR>\n" );
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document.write( "x = 200\r<BR>\n" );
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document.write( "So you need <font color=\"red\">200 liters</font> of the 10% solution\r<BR>\n" );
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document.write( "Now plug x = 200 into y = 300 - x to get\r<BR>\n" );
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document.write( "y = 300 - x\r<BR>\n" );
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document.write( "y = 300 - 200\r<BR>\n" );
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document.write( "y = 100\r<BR>\n" );
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document.write( "and you need <font color=\"red\">100 liters</font> of the 25% solution<BR>\n" );
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