document.write( "Question 1138294: a chef is going to use a mixture of two brands of italian dressing. the first brand contains 9% vinegar, and the second brand contains 14% vinegar. The chef wants to make 310 milliliters of a dressing that is 13% vinegar. How much of each brand should she use? \n" ); document.write( "

Algebra.Com's Answer #756126 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "In this problem, concentrations are the ratios of the pure vinegar volume to the total volume.\r\n" );
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document.write( "Let x be the amount of the 9%  vinegar needed (in milliliters), and\r\n" );
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document.write( "let y be the amount of the 14%  vinegar needed.\r\n" );
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document.write( "The amount of the \"pure\" vinegar in the 9% mixture  is 0.09x mL.\r\n" );
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document.write( "The amount of the \"pure\" vinegar in the 14% mixture is 0.14y mL.\r\n" );
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document.write( "The resulting mixture contains  0.09x + 0.14y mL of the pure vinegar and has the volume of 310 mL.\r\n" );
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document.write( "Thus you have these two equations\r\n" );
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document.write( "    x + y = 310    milliliters           (1)    (the total volume)\r\n" );
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document.write( "     = 0.13.                 (2)    (the resulting mixture concentration)\r\n" );
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document.write( "From equation  (1), express  x = 310 - y.  Substitute it into equation (2) and multiply both sides of this equation by 310. \r\n" );
document.write( "You will get\r\n" );
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document.write( "    0.09*(310-y) + 0.14y = 0.13*310.\r\n" );
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document.write( "From the last equation express y and calculate\r\n" );
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document.write( "    y =  = 248 mL of the 14% vinegar are needed.\r\n" );
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document.write( "Then from equation (1),  x = 310 - 248 = 62 mL of the 9% vinegar are needed.\r\n" );
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document.write( "Answer. 248 mL of the 14% vinegar  and  62 mL of the 9% vinegar are  needed.\r\n" );
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document.write( "Check.   = 0.13 = 13%.   ! Correct concentration !\r\n" );
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\n" ); document.write( "\n" ); document.write( "The problem is just solved.\r
\n" ); document.write( "\n" ); document.write( "I used 2-equation setup and the Substitution method.\r
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\n" ); document.write( "\n" ); document.write( "There are other solution methods, too.\r
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\n" ); document.write( "\n" ); document.write( "--------------\r
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\n" ); document.write( "\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( "    - Advanced mixture problems \r
\n" ); document.write( "\n" ); document.write( "    - Advanced mixture problem for three alloys \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( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\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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