document.write( "Question 1094062: How many gallons of a fruit drink that is 50% real juice must be mixed with a fruit drink that is 20% real juice to obtain 12 gallons of a fruit drink that is 40% real juice?\r
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\n" ); document.write( "\n" ); document.write( "x | .50 | .50x
\n" ); document.write( "12 | .40 | .40(12)
\n" ); document.write( "x+12 | .20 | .20(x+12) \n" ); document.write( "
Algebra.Com's Answer #708671 by ikleyn(52788)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "How many gallons of a fruit drink that is 50% real juice must be mixed with a fruit drink that is 20% real juice
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document.write( "Let \"x\" be the volume (in gallons) of the 50% real juice, which is under the question.\r\n" );
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document.write( "Then the volume of the 20% of the fruit juice to mix is 12-x gallons.\r\n" );
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document.write( "The volume of the pure juice in x gallons of 50% real juice is 0.5x gallons.\r\n" );
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document.write( "The volume of the pure juice in (12-x) gallons of 20% real juice is 0.2*(12-x)) gallons.\r\n" );
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document.write( "The total volume of the pure juice in the mix is the sum of these amounts, i.e.\r\n" );
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document.write( " 0.5x  + 0.2*(12-x) gallons.\r\n" );
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document.write( "The concentration of pure juice in the mixture is  this fraction \"%280.5x++%2B+0.2%2A%2812-x%29%29%2F12\".\r\n" );
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document.write( "According to the condition, it must be equal to 40%, or 0.4.\r\n" );
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document.write( "It gives you an equation \r\n" );
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document.write( "\"%280.5x++%2B+0.2%2A%2812-x%29%29%2F12\" = 0.4.\r\n" );
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document.write( "It is your governing equation to find x.\r\n" );
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document.write( "To solve it, multiply both sides by 12. You will get\r\n" );
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document.write( "0.5x + 0.2*(12-x) = 0.4*12,\r\n" );
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document.write( "0.5x + 2.4 - 0.2x = 4.8,\r\n" );
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document.write( "0.5x - 0.2x = 4.8 - 2.4,\r\n" );
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document.write( "0.3x = 2.4  ====>  x = \"2.4%2F0.3\" = \"24%2F3\" = 8.\r\n" );
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document.write( "Answer.  You need to use 8 gallons of 50% real juice and (12-8) = 4 gallons of 20% real juice.\r\n" );
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document.write( "Check.   8*0.5 + 4*0.2 = 4.8.   12*0.4 = 4.8.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "I prefer do not use the tables at all when solving such problems.
\n" ); document.write( "Simple logic leads you step by step along the solution from the beginning to the end, if you do know and understand this logic.\r
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\n" ); document.write( "\n" ); document.write( "Making table only distract you from the solution.\r
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\n" ); document.write( "\n" ); document.write( "But I do not insist that my way is the only applicable.\r
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\n" ); document.write( "\n" ); document.write( "I think that the tables play the role of crutches.\r
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\n" ); document.write( "\n" ); document.write( "If you do understand the logic, you do not need tables.\r
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\n" ); document.write( "\n" ); document.write( "And working to understand the logic is your goal.\r
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\n" ); document.write( "\n" ); document.write( "The way to it is practice.\r
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\n" ); document.write( "There is entire bunch of introductory lessons covering various types of mixture problems\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( "    - Word problems on mixtures for antifreeze solutions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for alloys \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( "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\r
\n" ); document.write( "\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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\n" ); document.write( "By the way, writing by @gosgarithmetic is I N C O R R E C T.\r
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