document.write( "Question 1155750: A sparkling-water distributor wants to make up 400 gal of sparkling water to sell for $ 8.00 per gallon. She wishes to mix three grades of water selling for $14.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as the $ 3.00 comma water. How many gallons of each should she use? \n" ); document.write( "

Algebra.Com's Answer #778419 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " This problem is, actually, can be solved using one single equation for one unknown.\r
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document.write( "Let x = the amount (the volume) of the $3 grade water, in gallons.\r\n" );
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document.write( "Then the amount of the $4.50 grade water is 2x gallons,\r\n" );
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document.write( "and  the amount of the $14 grade water is the rest  (400 - x - 2x) = (400-3x)  gallons.\r\n" );
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document.write( "The money equation is\r\n" );
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document.write( "    3x + 4.50*(2x) + 14*(400-3x) = 8*400   dollars.\r\n" );
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document.write( "Simplify and solve for x\r\n" );
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document.write( "    3x + 9x + 14*400 - 42x = 8*400\r\n" );
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document.write( "    -30x                   = 8*400 - 14*400\r\n" );
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document.write( "     x  =  =   80.\r\n" );
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document.write( "ANSWER.  80 gallons of the $3 grade water;  2*80 = 160 gallons of the $4.50 grade water \r\n" );
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document.write( "         and the rest, (400-80-160) = 160 gallons of the $14 grade water.\r\n" );
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document.write( "CHECK.   3*80 + 160*4.50 + 14*160 = 3200 dollars, same as 8*400 = 3200 dollars.    ! Precisely correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "At this site, there is a SPECIAL LESSON explaining and showing how to solve different similar problems in the same way\r
\n" ); document.write( "\n" ); document.write( " - Advanced word problems to solve using a single linear equation\r
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document.write( "   +-------------------------------------------------------+\r\n" );
document.write( "   |   THIS ADDITION IS TO ALL OTHER TUTORS AT THIS FORUM  |\r\n" );
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document.write( "My older grandson is now a second year Stanford university student.\r\n" );
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document.write( "Couple of weeks ago I gave him similar problem, that came to the forum.\r\n" );
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document.write( "My goal was to check if he knows this method (reducing to single equation in one unknown).\r\n" );
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document.write( "Surely, he easily solved the problem. What is MORE INTERESTING, he solved it using EXACTLY THIS METHOD.\r\n" );
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document.write( "I then asked him, if the Math teacher explained this method to them in his school.\r\n" );
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document.write( "\"YES\", he answered, \"in my 6-th or 7-th grade\".\r\n" );
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document.write( "He was at a regular middle school that time.\r\n" );
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document.write( "I, at my same age, was also touched to this method (although in other country). \r\n" );
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document.write( "So  now I am 179% sure/confident  that it is exactly the method to teach the students of this grade.\r\n" );
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document.write( "(Before I was only 129% sure).\r\n" );
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document.write( "    Similar problems came MANY TIMES to this forum.\r\n" );
document.write( "    Many times I explained here, at the forum, the method of their solution.\r\n" );
document.write( "    I do not think that my solutions went out of you . . . \r\n" );
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document.write( "    Surely, we live in the democratic country, and I can not dictate to you on how present your solutions to the forum \r\n" );
document.write( "        (UNFORTUNATELY :)\r\n" );
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document.write( "    But when you teach the students differently, you simply miss an opportubity to teach them in a right way (!)\r\n" );
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document.write( "    Please keep it in  mind (!)\r\n" );
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