document.write( "Question 1184008: How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 60% antifreeze? Use the six- step method \n" ); document.write( "
Algebra.Com's Answer #814536 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 10% antifreeze
\n" ); document.write( "to get a mixture that is 60% antifreeze? Use the six- step method
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\n" ); document.write( "\n" ); document.write( "            I don't know what the six-step method is;
\n" ); document.write( "            therefore, I will solve the problem following to a standard procedure and common sense.\r
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document.write( "100 gallons of 10% antifreeze contain 0.1*100 = 10 gallons of pure antifreeze.\r\n" );
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document.write( "If we add x gallons of the 70% of the antofreeze solution, the total liquid volume will be 100+x gallons,\r\n" );
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document.write( "and the content of antifreeze in it will be  10+0.7x  gallons.\r\n" );
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document.write( "Now, the concentration of the antifreeze in the new mixture is  C = \"%2810%2B0.7x%29%2F%28100%2Bx%29\"  gallons of antifreeze\r\n" );
document.write( "per gallon of the mixture.\r\n" );
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document.write( "It gives an equation to find x\r\n" );
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document.write( "    \"%2810%2B0.7x%29%2F%28100%2Bx%29\" = 0.6.\r\n" );
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document.write( "To solve it, multiply both sides by (100+x) to get\r\n" );
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document.write( "    10+0.7x = 0.6*(100+x).\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    10 + 0.7x = 60 + 0.6x\r\n" );
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document.write( "    0.7x - 0.6x = 60 - 10\r\n" );
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document.write( "        0.1x    =    50\r\n" );
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document.write( "         x      =    50/0.1 = 500.\r\n" );
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document.write( "ANSWER.  500 gallon of the 70% antifreeze solution should be added.\r\n" );
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document.write( "CHECK.   \"%280.7%2A500+%2B+0.1%2A100%29%2F%28500%2B100%29\" = 0.6 = 60%.    ! Correct concentration !\r\n" );
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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( "In this site, there is a bunch of lessons,  covering various types of mixture problems.  See introductory lessons\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( "    - Word problems on mixtures for antifreeze solutions \r
\n" ); document.write( "\n" ); document.write( "    - Typical word problems on mixtures from the archive\r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution the mixture word problems.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Mixture problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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