document.write( "Question 1150928: A 10% salt solution is to be mixed with pure water to produce 45 gallons of a 3% salt solution. How much of each are needed? \n" ); document.write( "

Algebra.Com's Answer #772511 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "The first and the major step in solving such problems is to understand what is a 10% salt solution  and what is a 3% salt solution.\r\n" );
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document.write( "The concentration in such problems is measured in kilograms of salt per liter of the mixture.\r\n" );
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document.write( "A 10% salt solution is 1 liter of water with dissolved 100 grams of salt in it - or any proportional mixture.    (1)\r\n" );
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document.write( "A 3% salt solution is 1 liter of water with dissolved 30 grams of salt in it - or any proportional mixture.      (2)\r\n" );
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document.write( "    These are not unique possible definitions.\r\n" );
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document.write( "    One can define a 10% salt solution as a mixture that contains 10% of salt by weight (by total mass of the solution).\r\n" );
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document.write( "    It is not exactly the same definition as (1) - these two definitions are slightly different.\r\n" );
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document.write( "    But in school Math, students and teachers usually NEGLECT this difference,\r\n" );
document.write( "    and consider and accept (1) and (2) as the basic definitions.\r\n" );
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document.write( "So, taking into account that 1 gallon = 3.785 liters, we can say that 45 gallons of 3% salt solution contain\r\n" );
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document.write( "      45*3.785*0.03 kilograms of salt.    (3)\r\n" );
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document.write( "Since we obtained these 45 gallons of the 3% salt solution by adding water,\r\n" );
document.write( "our original 10% salt solution contained exactly this (= the same) amount (3) of salt.\r\n" );
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document.write( "Hence, the volume of the original 10% salt solution was \r\n" );
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document.write( "     volume =  =  = 45*3.785*0.3 liters.\r\n" );
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document.write( "It means that the volume of water added is the difference\r\n" );
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document.write( "    volume of water added = 45*3.785 - 45*3.785*0.3 liters = 45*3.785*(1-0.3) = 45*3.785*0.7 liters.    (4)\r\n" );
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document.write( "If you want to express this volume in gallons, you must divide (4) by the conversion factor of 3.785.\r\n" );
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document.write( "Thus the volume of water to add in gallons is  45*0.7 = 31.5 gallons.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "For introductory lessons covering various types of mixture word problems see\r
\n" ); document.write( "\n" ); document.write( "    - Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - More Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical word problems on mixtures for solutions \r
\n" ); document.write( "\n" ); document.write( "    - Typical word problems on mixtures from the archive\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "You will find there ALL TYPICAL mixture problems with different methods of solutions,
\n" ); document.write( "explained at different levels of detalization, from very detailed to very short.\r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution mixture word problems.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook in the section \"Word problems\" under the topic \"Mixture problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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