document.write( "Question 1204664: a nurse wants to make 50 ml of a 20% morphine solution. she needs to mix 10% morphine solution with 50% morphine solution to make this happen. how many ml of each must she mix? \n" ); document.write( "

Algebra.Com's Answer #841065 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a nurse wants to make 50 ml of a 20% morphine solution.
\n" ); document.write( "she needs to mix 10% morphine solution with 50% morphine solution to make this happen.
\n" ); document.write( "how many ml of each must she mix?
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document.write( "Let x be the the volume of the 50% morphine solution to use, in milliliters.\r\n" );
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document.write( "Then the volume of the 10% solutions of morphine is (50-x) mL,\r\n" );
document.write( "to make the total volume of 50 mL.\r\n" );
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document.write( "The 50% solution contributes  0.5x mL       of the pure morphine to the final mixture.\r\n" );
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document.write( "The 10% solution contributes  0.1*(50-x) mL of the pure morphine to the final mixture.\r\n" );
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document.write( "So, the total amount of the pure morphine in 50 Ml of the final mixture is\r\n" );
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document.write( "    0.5x + 0.1*(50-x)  milliliters.\r\n" );
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document.write( "We want this amount of the pure morphine provides 20% final solution.\r\n" );
document.write( "So, we write this equation, which describes it\r\n" );
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document.write( "     = 0.2.\r\n" );
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document.write( "Simplify it by multiplying both sides by 50\r\n" );
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document.write( "    0.5x + 0.1*(50-x) = 0.2*50.\r\n" );
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document.write( "Simplify further and express x\r\n" );
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document.write( "    0.5x + 5 - 0.1x = 10\r\n" );
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document.write( "    0.5x - 0.1x = 10 - 5\r\n" );
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document.write( "        0.4x    =    5\r\n" );
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document.write( "           x    =    5/0.4 = 12.5.\r\n" );
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document.write( "ANSWER.  12.5 mL of the 50% morphine solution and 50-12.5 = 37.5 ml of the 10% morhine solution should be used.\r\n" );
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document.write( "CHECK.    = 0.2, or 20% concentration of the final solution.   ! 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( "It is a standard and typical mixture problem.\r
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\n" ); document.write( "\n" ); document.write( "For introductory lessons covering various types of mixture word problems see\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( "    - Typical word problems on mixtures from the archive\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "You will find there ALL TYPICAL mixture problems with different methods of solutions,
\n" ); document.write( "explained at different levels of detalization, from very detailed to very short.\r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution mixture word problems.\r
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