document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947566>Question 947566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q. How much salt should be added to 60 litres of a 20% solution of salt to increase it to a 40 % solution of salt?\r<BR>\n" );
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document.write( "Do you think you can frame the equations too? How do i convert 20% of salt to measurements (ie grams or kilograms)\r<BR>\n" );
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document.write( "i was thinking (60 + x) 40/100 = ....<BR>\n" );
document.write( "Im really confused, since its a salt solution. Im in 8th grade, kindly explain in a way that is understandable to me. Thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578221 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=578221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the question is:\r<BR>\n" );
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document.write( "How much salt should be added to 60 litres of a 20% solution of salt to increase it to a 40 % solution of salt? \r<BR>\n" );
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document.write( "20% of 60 liters is equal to 12 liters.\r<BR>\n" );
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document.write( "the solution has 12 liters of salt and 48 liters of some other substance.\r<BR>\n" );
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document.write( "we can assume they are talking about volume here, since the measurement is in liters which is a volume type measurement.\r<BR>\n" );
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document.write( "we'll let x represent the amount of salt that has to be added to the solution.\r<BR>\n" );
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document.write( "out equation will be .20 * 60 + x = .40 * (60 + x).\r<BR>\n" );
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document.write( "solve this equation for x and you will have the number of liters of salt that has to be added.\r<BR>\n" );
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document.write( "start with .20 * 60 + x = .40 * (60 + x)\r<BR>\n" );
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document.write( "simplify to get 12 + x = .40 * 60 + .40 * x\r<BR>\n" );
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document.write( "simplify further to get 12 + x = 24 + .4x\r<BR>\n" );
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document.write( "subtract 12 from both sides of this equation and subtract .4x from both sides of this equation to get .6x = 12\r<BR>\n" );
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document.write( "divide both sides of this equation by .6 to get x = 12/.6\r<BR>\n" );
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document.write( "simplify to get x = 20\r<BR>\n" );
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document.write( "you would need to add 20 liters of salt to the 20% mixture in order to get a 40% mixture.\r<BR>\n" );
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document.write( "the formula of .20 * 60 + x = .40 * (60 + x) becomes:\r<BR>\n" );
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document.write( "12 + 20 = .40 * (60 + 20) which becomes;\r<BR>\n" );
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document.write( "32 = .4 * 80 which becomes:\r<BR>\n" );
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document.write( "32 = 32\r<BR>\n" );
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document.write( "since the equation is true, the solution of x = 20 is correct.\r<BR>\n" );
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document.write( "that's easy to see because, if you add 20 to 12 you get 32, and if you add 20 to 60 you get 80 and it's clear that 32 / 80 is equal to .4 which is equal to 40%.\r<BR>\n" );
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document.write( "the weight of the salt doesn't enter the problem.\r<BR>\n" );
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document.write( "however, there are probably some conversion tables that can tell you the weight of salt by volume.\r<BR>\n" );
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document.write( "one such conversion table told me that the density of salt is 2170 grams per liter of volume of salt.\r<BR>\n" );
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document.write( "if it is dissolved in a liquid, then some other conversion factors would apply.\r<BR>\n" );
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document.write( "here's an excerpt from a google search i did on density of salt.\r<BR>\n" );
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document.write( "The molar mass of salt is 58.443 g/mol, its melting point is 801 °C (1,474 °F) and its boiling point 1,465 °C (2,669 °F). Its density is 2.17 grams per cubic centimetre and it is readily soluble in water. When dissolved in water it separates into Na+ and Cl&#8722; ions and the solubility is 359 grams per litre.\r<BR>\n" );
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document.write( "the bottom line on the problem, however, has nothing to do with the density of the salt.\r<BR>\n" );
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document.write( "20% of 60 liters is 12 liters of salt.\r<BR>\n" );
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document.write( "40% of 80 liters is 32 liters of salt.\r<BR>\n" );
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document.write( "if you start with 60 liters that is 20% salt by volume, then you need to add 20 liters of salt to get 80 liters that is 40% salt by volume.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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