document.write( "Question 1203315: The Royal Fruit Company produces two types of fruit drinks. The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 35% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 35% pure fruit juice? \n" ); document.write( "

Algebra.Com's Answer #838767 by ikleyn(52784) $\"\"$ $\"About$

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\n" ); document.write( "The Royal Fruit Company produces two types of fruit drinks.
\n" ); document.write( "The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice.
\n" ); document.write( "The company is attempting to produce a fruit drink that contains 35% pure fruit juice.
\n" ); document.write( "How many pints of each of the two existing types of drink must be used to make
\n" ); document.write( "50 pints of a mixture that is 35% pure fruit juice?
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document.write( "     x     pints  of the 70% juice,\r\n" );
document.write( "and (50-x) pints  of the 20% juice.\r\n" );
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document.write( "x      pints of the 70% juice contain  0.7x      pints of the pure juice;\r\n" );
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document.write( "(50-x) pints of the 20% juice contain  0.2(50-x) pints of the pure juice.\r\n" );
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document.write( "50 pints of the final mixture contain 0.35*50    pints of the pure juice.\r\n" );
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document.write( "When we chose this presentation of ingredients, x and (50-x) pints, we just provided \r\n" );
document.write( "the total volume of the mixture of x + (50-x) = 50 pints.\r\n" );
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document.write( "The only condition which remained and which we should satisfy was to make a balance \r\n" );
document.write( "of the pure juice in ingredients and in the final mixture.\r\n" );
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document.write( "So, we write this equation for the pure juice amounts\r\n" );
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document.write( "    0.7x + 0.2*(50-x) = 0.35*50   pints of the pure juice.\r\n" );
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document.write( "Simplify the equation and find x\r\n" );
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document.write( "    0.7x + 10 - 0.2x = 17.5\r\n" );
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document.write( "    0.7x - 0.2x = 17.5 - 10\r\n" );
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document.write( "       0.5x     =  7.5\r\n" );
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document.write( "          x     =  7.5/0.5 = 15  pints.\r\n" );
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document.write( "ANSWER.  15 pints of the  70% juice and (50-15) = 35 pints of the 20% juice.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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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
\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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