document.write( "Question 1145595: Suppose you want to fill nine 1-lb tins with a snack mix. You have $15 and plan to buy almonds for $2.45 per lb, hazelnuts for $1.85 per lb, and raisins for $.80 per lb. You want the mix to contain twice as much lf the nuts as the raisins by weight. How much of each ingredient should you buy?
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Algebra.Com's Answer #766831 by ikleyn(52830) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Suppose you want to fill nine 1-lb tins with a snack mix. You have $15 and plan to buy almonds for $2.45 per lb,
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\n" ); document.write( " $\"highlight%28cross%28lf%29%29\"$ lb the nuts as the raisins by weight. How much of each ingredient should you buy?
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\n" ); document.write( "\n" ); document.write( "            From the first glance, this problem is for 3 equations in three unknowns.\r
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\n" ); document.write( "\n" ); document.write( "            But actually, it can be easily solved using only ONE single equation in ONE unknown.\r
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\n" ); document.write( "\n" ); document.write( "            I will show you how to do it.\r
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document.write( "Let  x be the amount of raisins by weight, in pounds.\r\n" );
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document.write( "Then the amount of the nuts is 2x pounds, according to the condition.\r\n" );
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document.write( "And the amount of almonds is then the rest (9-x-2x) = 9-3x.\r\n" );
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document.write( "The total cost equation is then\r\n" );
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document.write( "    0.80*x + 1.85*(2x) + 2.45*(9-3x) = 15.00    dollars.\r\n" );
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document.write( "Simplify and solve for x :\r\n" );
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document.write( "    0.80x + 3.70x + 2.45*9 - 7.35x = 15.00,\r\n" );
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document.write( "      x                      =  = 2.47 pounds of raisins.\r\n" );
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document.write( "ANSWER.  2.47 pounds of raisins;  2*2.47 = 4.94 pounds of nuts, and the rest (9 - 3*2.47) = 1.59 pounds of almonds.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The benefit of this approach is that students may start solving such problems much earlier than they start learning systems of equations.\r
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\n" ); document.write( "\n" ); document.write( "I think that the true goal of this problem is to teach students to this approach.\r
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\n" ); document.write( "\n" ); document.write( "If you do not like these ugly number in the answer, then double check your input (!)\r
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\n" ); document.write( "\n" ); document.write( "To see other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - More complicated word problems to solve using a single linear equation \r
\n" ); document.write( "\n" ); document.write( "    - Advanced word problems to solve using a single linear equation\r
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\n" ); document.write( "\n" ); document.write( "Be aware ! :   the setup in the post by @josgarithmetic is INCORRECT !\r
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