document.write( "Question 1202720: The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $5 per pound with some Orange Pekoe tea that sells for $2 per pound to get 300 pounds of the new blend. The selling price of the new blend is to be $2.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?\r
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Algebra.Com's Answer #837788 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "The manager of a store that specializes in selling tea decides to experiment
\n" ); document.write( "with a new blend. She will mix some
\n" ); document.write( "Earl Grey tea that sells for $5 per pound with some
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\n" ); document.write( "to get 300 pounds of the new blend.
\n" ); document.write( "The selling price of the new blend is to be $2.50 per pound,
\n" ); document.write( "and there is to be no difference in revenue from selling the new blend versus
\n" ); document.write( "selling the other types.
\n" ); document.write( "How many pounds of the Earl Grey tea and Orange Pekoe tea are required?
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\n" ); document.write( "\n" ); document.write( "        It can be solved using one equation in one single unknown,
\n" ); document.write( "        or using a system of equations in two unknowns.
\n" ); document.write( "        I will show you the solution using one equation,
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document.write( "Let x be the pounds of the Earl Grey tea;\r\n" );
document.write( "then the pounds of the Orange Pekoe tea is (300-x) pounds.\r\n" );
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document.write( "x pounds per $5 per pound contribute 5x dollars to the cost of the mixture.\r\n" );
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document.write( "(300-x) pounds per $2 per pound contribute 2(300-x) dollars to the cost of the mixtire.\r\n" );
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document.write( "For total cost, we obtain this equation\r\n" );
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document.write( "    5x + 2*(300-x) = 2.50*300    (1)\r\n" );
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document.write( "The right side is the cost of 300 pounds of the mixture at given cost $2.50 per pound.\r\n" );
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document.write( "Simplify this equation and find x\r\n" );
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document.write( "    5x + 600 - 2x = 750\r\n" );
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document.write( "    5x - 2x = 750 - 600\r\n" );
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document.write( "       3x   =    150\r\n" );
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document.write( "        x   =    150/3 = 50 pounds.\r\n" );
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document.write( "ANSWER.  50 pounds of the Earl Grey tea and 300-50 = 250 pounds of the Orange Pekoe tea.\r\n" );
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document.write( "CHECK.   5*50 + 2*250 = 750 dollars, the cost of the ingredients.\r\n" );
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document.write( "         2.50*300 = 750 dollars, the cost of the mixture.\r\n" );
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document.write( "         The cost is the same for the ingredients and the mixture;\r\n" );
document.write( "         hence, the solution is CORRECT.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see on how to solve similar problems using two equations and two unknowns, look into the lessons\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
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