document.write( "Question 1156558: How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution?\r
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Algebra.Com's Answer #779285 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Let x be the amount of the 20% alcohol solution (in gallons),\r\n" );
document.write( "and y be the amount of the 50% alcohol solution.\r\n" );
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document.write( "Your first equation is\r\n" );
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document.write( "    x + y = 9                      (1)\r\n" );
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document.write( "for the total volume.\r\n" );
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document.write( "There are 0.2x gallons of the pure alcohol in the x gallons of the 20% solution,\r\n" );
document.write( "and there are 0.5y gallons of the pure alcohol in the y gallons of the 50% solution.\r\n" );
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document.write( "So, there are, in total, 0.2x + 0.5y gallons of the pure alsohol in ingredients.\r\n" );
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document.write( "It should be equal to the amount of the the pure alcohol in the mixture,  0.3*9.\r\n" );
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document.write( "It gives you the second equation\r\n" );
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document.write( "    0.2x + 0.5y = 0.3*9    gallons   (2)\r\n" );
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document.write( "Thus you have the system of two equations, (1) and (2).\r\n" );
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document.write( "From equation (1), express  x = 9-y and substitute it into the second equation, replacing x You will get\r\n" );
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document.write( "    0.2*(9-y) + 0.5y = 2.7.\r\n" );
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document.write( "From this equation\r\n" );
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document.write( "    y =  = 3.\r\n" );
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document.write( "So, the problem is just solved.\r\n" );
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document.write( "ANSWER.  3 gallons of the 50% solution, and the rest, (9-3) = 6 gallons of the 20% solution.\r\n" );
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document.write( "CHECK.   I will calculate the concentration of the mixture. It is   = 0.3 = 30%.   ! Precisely correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical mixture problem.\r
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\n" ); document.write( "\n" ); document.write( "For introductory lessons covering various types of mixture word problems see\r
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\n" ); document.write( "\n" ); document.write( "    - More Mixture problems\r
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\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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