document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98236>Question 98236</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201312247/algebrahomeworkh>   Intermediate Algebra through Applications</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> As part of a lab experiment for your chemistry class, you add pure alcohol to 24 ml of a 9% solution.  How much pure alcohol must you add to the 9% solution to make a 16% solution?\r<BR>\n" );
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document.write( "My professor was showing us how to set up charts to help solve the problems and I don't know where to begin.  I just need help setting up a chart and then I could solve the problem.  -Thanks   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71393 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20059)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=71393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><b>As part of a lab experiment for your chemistry class, you add pure alcohol to\r\n" );
document.write( "24 ml of a 9% solution. How much pure alcohol must you add to the 9% solution\r\n" );
document.write( "to make a 16% solution? \r\n" );
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document.write( "My professor was showing us how to set up charts to help solve the problems and\r\n" );
document.write( "I don't know where to begin. I just need help setting up a chart and then I\r\n" );
document.write( "could solve the problem. -Thanks \r\n" );
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document.write( "There are many ways to make a chart. Below is one way, but your professor\r\n" );
document.write( "might use another one.\r\n" );
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document.write( "Think of each liquid as containing part alcohol and the rest water.\r\n" );
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document.write( "Let the 24 ml. of 9% solution be called the \"first\" liquid.\r\n" );
document.write( "Let the pure alcohol be called the \"second\" liquid. When we\r\n" );
document.write( "mix them we will call that the \"final\" liquid.\r\n" );
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document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid                                                          \r\n" );
document.write( "Second liquid                                                 \r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid                                                 \r\n" );
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document.write( "Let the number of milliliters of pure alcohol we need to add be x.\r\n" );
document.write( "So let's place x for the number of milliliters of the second liquid.\r\n" );
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document.write( "     \r\n" );
document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid                                                          \r\n" );
document.write( "Second liquid          x                                      \r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid                                                  \r\n" );
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document.write( "We are told we have 24 liters of the first liquid, so we fill\r\n" );
document.write( "in 24 for the number of milliliters of the first liquid:\r\n" );
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document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24                                              \r\n" );
document.write( "Second liquid          x                                       \r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid                                                  \r\n" );
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document.write( "Now we will figure how many milliliters of alcohol the first\r\n" );
document.write( "liquid contains.  Since it is 9% alcohol we multiply .09 by\r\n" );
document.write( "24 and get 2.16 ml of alcohol in the first liquid, so we fill\r\n" );
document.write( "in 2.16 for the number of milliliters of alcohol in the first liquid.\r\n" );
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document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24               2.16                           \r\n" );
document.write( "Second liquid          x                                     \r\n" );
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document.write( "Final liquid                                                 \r\n" );
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document.write( "The rest of the 24 milliliters is water, so we subtract 2.16 from\r\n" );
document.write( "24 to get 21.84 milliliters of water.  So we fill in 21.84 as the \r\n" );
document.write( "number of milliliters of water in the first liquid.\r\n" );
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document.write( "                   milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24               2.16            21.84          \r\n" );
document.write( "Second liquid          x                                        \r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid                                            \r\n" );
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document.write( "Next since the x milliliters of the second liquid is pure alcohol,\r\n" );
document.write( "then it contains x milliliters of alcohol. So fill in x also for \r\n" );
document.write( "the number of milliliters of alcohol in the second liquid \r\n" );
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document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24               2.16            21.84          \r\n" );
document.write( "Second liquid          x                  x             \r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid                                                  \r\n" );
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document.write( "Now since there is no water in the second liquid (since it is all\r\n" );
document.write( "pure alcohol) we enter zero for the number of milliliters of water\r\n" );
document.write( "in the second liquid.\r\n" );
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document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24               2.16            21.84          \r\n" );
document.write( "Second liquid          x                  x             0.00\r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid         \r\n" );
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document.write( "Now to get the total number of milliliters of the final liquid, \r\n" );
document.write( "we add the 24 and the x and get 24+x, so we fill that in\r\n" );
document.write( "for the number of millilters of liquid in the final liquid.\r\n" );
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document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24               2.16            21.84          \r\n" );
document.write( "Second liquid          x                  x             0.00\r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid         24+x            \r\n" );
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document.write( "Now to get the total number of milliliters of alcohol in the final\r\n" );
document.write( "liquid, we add the 2.16 and the x and get 2.16+x, so we fill that in\r\n" );
document.write( "for the number of millilters of alcohol in the final liquid.\r\n" );
document.write( "\r\n" );
document.write( "                  milliliters of   mililiters of   mililiters of \r\n" );
document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24               2.16            21.84          \r\n" );
document.write( "Second liquid          x                  x             0.00\r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid         24+x            2.16+x            \r\n" );
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document.write( "Now to get the total number of milliliters of water in the final\r\n" );
document.write( "liquid, we add the 21.84 and the 0.00 and get 21.84, so we fill \r\n" );
document.write( "that in for the number of millilters of alcohol in the final \r\n" );
document.write( "liquid.\r\n" );
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document.write( "                     liquid           alcohol          water    \r\n" );
document.write( "                        \r\n" );
document.write( "First liquid          24               2.16            21.84          \r\n" );
document.write( "Second liquid          x                  x             0.00\r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "Final liquid         24+x            2.16+x            21.84\r\n" );
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document.write( "Now to get the equation, we reason this way:\r\n" );
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document.write( "The number of milliliters of alcohol in the final mixture is 16% of\r\n" );
document.write( "the number of milliliters of liquid in the final mixture.\r\n" );
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document.write( "or\r\n" );
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document.write( "2.16+x is 16% of 24+x\r\n" );
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document.write( "\"is\" means \"equals\"\r\n" );
document.write( "\"16%\" means \".16\"\r\n" );
document.write( "\"of\" means \"times\" \r\n" );
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document.write( "So the equation is\r\n" );
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document.write( "2.16+x = .16(24+x)\r\n" );
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document.write( "Solve that and get  x = 2 milliliters of the second\r\n" );
document.write( "liquid which is pure alcohol.\r\n" );
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document.write( "Notice that you don't really need to have the column\r\n" );
document.write( "for the number of milliliters of water, for it doesn't\r\n" );
document.write( "enter into the equation.  However I included it in \r\n" );
document.write( "order to break down the thinking process for you. You\r\n" );
document.write( "may omit the \"miililiters of water\" column from your\r\n" );
document.write( "work.\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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