document.write( "Question 1180566: A gasoline refinery mixes different types of gasoline. How many gallons of grade A worth 17.60 per gallon must be mixed with grade B worth 19.20 per gallon and grade C at 22.40 per gallon to produce 10 gallons of gas that will sell for 19.52 per gallon if equal amount of grade A and C are mixed?\r
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Algebra.Com's Answer #810293 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A gasoline refinery mixes different types of gasoline. How many gallons of grade A worth 17.60 per gallon
\n" ); document.write( "must be mixed with grade B worth 19.20 per gallon and grade C at 22.40 per gallon to produce 10 gallons of gas
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\n" ); document.write( "\n" ); document.write( "            From the first glance, this problem is for 3 unknowns and 3 equations.\r
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\n" ); document.write( "\n" ); document.write( "            Edwin managed to reduce it to two unknowns in two equations.\r
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\n" ); document.write( "\n" ); document.write( "            I will go FURTHER and will show you even MORE SIMPLE way to solve the problem using only ONE unknown and ONE equation.\r
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\n" ); document.write( "\n" ); document.write( "            Watch attentively every my step.\r
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\n" ); document.write( "\n" ); document.write( "            You may feel yourself shocked. Do not worry - it is very natural feeling for those who see this trick for the first time.\r
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document.write( "Let x be the amount (the volume in gallons) of the grade A.\r\n" );
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document.write( "The amount of the grade C is the same x gallons as the grade A, according to the condition.\r\n" );
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document.write( "Hence, the amount of the grade B is the rest  (10-2x) gallons.\r\n" );
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document.write( "Now we write the total cost equation\r\n" );
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document.write( "    17.60x + 19.20*(10-2x) + 22.40x = 10*19.52.\r\n" );
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document.write( "I think that you do not need long explanations regarding this equation: you write it as you read the problem.\r\n" );
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document.write( "The only thing to explain is the right side, which is the cost of 10 gallons of the mixture.\r\n" );
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document.write( "Now simplify and solve this equation\r\n" );
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document.write( "    17.60x - 19.20*10 - 19.20*2x + 22.40x = 10*19.52\r\n" );
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document.write( "               1.6x                       = 10*19.52 - 19.20*10\r\n" );
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document.write( "               1.6x                       = 3.2\r\n" );
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document.write( "                  x                       = 3.2/1.6 = 2.\r\n" );
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document.write( "So, the problem is just solved:  you need 2 gallons of the grade A,  2 gallons of the grade C \r\n" );
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document.write( "                                 and the rest (10 - 2 - 2) = 6 gallons is the grade B.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and carefully explained.\r
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\n" ); document.write( "\n" ); document.write( "Now estimate the advantages of my method:\r
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\r\n" );
document.write( "    - you do not need to draw this table of the components (which I hate to spend my time preparing it);\r\n" );
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document.write( "    - you do not need solve NEITHER system of three equations NOR system of two equations;\r\n" );
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document.write( "    - and even 6-th or 7-th grade student can solve it easily . . . if he or she knows the method.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now I will tell you what other people do not know:\r
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\n" ); document.write( "\n" ); document.write( " 1) This problem is DESIGNED and is INTENDED to be solved by this method.\r
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\n" ); document.write( "\n" ); document.write( " 2) And this method is the EXPECTED WAY to solve and expected way TO TEACH students solving such and similar problems.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
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