document.write( "Question 1168985: A t-shirt design company is dying purple shirts for a school club. The shirts came out too light so the company needs to add more pure blue dye to the mixture to get a darker purple color for the shirts. The full vat of color holds 54 gallons of the original dye that is 27% blue. How many gallons should be drained and replaced with pure blue dye so that the mixture will be 40% blue? \n" ); document.write( "
Algebra.Com's Answer #793630 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "A t-shirt design company is dying purple shirts for a school club. The shirts came out too light so the company needs to add
\n" ); document.write( "more pure blue dye to the mixture to get a darker purple color for the shirts. The full vat of color holds 54 gallons
\n" ); document.write( "of the original dye that is 27% blue. How many gallons should be drained and replaced with pure blue dye so that the mixture will be 40% blue?
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document.write( "Let V be the volume to drain off from 54 gallons of the 27% solution.\r\n" );
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document.write( "Step 1:  Draining.  After draining,  you have (54-V) gallons of the 27% acid solution.\r\n" );
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document.write( "Step 2:  Replacing.  Then you add V gallons of the pure blue dye (the replacing step).\r\n" );
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document.write( "                     After the replacing,  you have the same total liquid volume of 54 gallons.\r\n" );
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document.write( "It contains  0.27*(54-V) + V   of pure blue dye.\r\n" );
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document.write( "So, your \"concentration equation\" is\r\n" );
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document.write( "    \"%280.27%2A%2854-V%29+%2B+V%29%2F54\" = 0.4.    (1)\r\n" );
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document.write( "At this point, the setup is done and completed.\r\n" );
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document.write( "Now you need to solve your basic equation  (1).\r\n" );
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document.write( "As the first step, multiply both sides by 80, and then simplify\r\n" );
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document.write( "    0.27*(54-V) + V = 0.4*54\r\n" );
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document.write( "    14.58 - 0.27V + V = 21.6\r\n" );
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document.write( "    0.73V = 21.6 - 14.58 = 7.02\r\n" );
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document.write( "    V = \"7.02%2F0.73\" = 9.616.\r\n" );
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document.write( "ANSWER.  9.616 gallons of the 27% solution should be drained and replaced by the pure blue duy.\r\n" );
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document.write( "CHECK.   \"%280.27%2A%2854-9.616%29+%2B+9.616%29%2F54\" = 0.4.    ! Precisely correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is entire bunch of 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 dry substances like coffee beans, nuts, cashew and peanuts\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for dry substances like candies, dried fruits\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for dry substances like soil and sand\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( "    - Advanced mixture problems \r
\n" ); document.write( "\n" ); document.write( "    - Advanced mixture problem for three alloys \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on word problems for mixtures\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "A convenient place to quickly observe these lessons from a  \"bird flight height\"  (a top view)  is the last lesson in the list.\r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution the mixture word problems.\r
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\n" ); document.write( "\n" ); document.write( "Specially for \"draining - replacing\" mixture problems see the lesson marked (*) in the list.\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 online textbook 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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