document.write( "Question 1056579: A taxidermist has a container with a solution of 10% tanning chemical and a container with a solution of 50% tanning chemical. If the taxidermist wants to mix the solutions to get 10 gallons of the solution with 25% tanning chemical, how many gallons of each solution should be mixed? \n" ); document.write( "

Algebra.Com's Answer #671741 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A taxidermist has a container with a solution of 10% tanning chemical and a container with a solution of 50% tanning chemical.
\n" ); document.write( "If the taxidermist wants to mix the solutions to get 10 gallons of the solution with 25% tanning chemical,
\n" ); document.write( "how many gallons of each solution should be mixed?
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\n" ); document.write( "\n" ); document.write( "Solution 1. Two equations\r
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document.write( "Let \"t\" be the volume of the 10% tanning chemical to mix (in gallons), and\r\n" );
document.write( "let \"f\" be the volume of the 50% tanning chemical to mix (in gallons).\r\n" );
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document.write( "Then you have these two equations\r\n" );
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document.write( "   t +    f = 10,        (1)    for the total volume\r\n" );
document.write( "0.1t + 0.5f = 0.25*10    (2)    for the pure chemical amount.\r\n" );
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document.write( "Multiply (2) by 10. You will get\r\n" );
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document.write( "   t +    f = 10,        (1')   ( still (1) )\r\n" );
document.write( "   t +   5f = 2.5*10     (2') \r\n" );
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document.write( "Now distract (1') from (2') (both sides). You will get\r\n" );
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document.write( "   5f - f = 25 - 10,\r\n" );
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document.write( "   4f = 15   --->  f = .\r\n" );
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document.write( "Thus you just found the volume of the 50% solution. It is  gallons. \r\n" );
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document.write( "Then the volume of the 10% solution is t =  =  =  gallons.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2. One equation.\r
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document.write( "This equation is\r\n" );
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document.write( "0.1t + 0.5*(10-t) = 0.25*10.\r\n" );
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document.write( "Simplify and solve for \"t\":  t = , the same answer.\r\n" );
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