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( "

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\n" ); document.write( "Batch A: 10% morphine
\n" ); document.write( "Batch B: 50% morphine
\n" ); document.write( "Target concentration: 20% morphine\r
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\n" ); document.write( "\n" ); document.write( "The gap from 10% to 20% is 10
\n" ); document.write( "The gap from 20% to 50% is 30
\n" ); document.write( "The ratio 10:30 reduces to 1:3\r
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\n" ); document.write( "\n" ); document.write( "The nurse will need 3 times as much of one solution compared to the other.
\n" ); document.write( "The ratio 1:3 scales up to 1x:3x for some positive real number x.
\n" ); document.write( "Add up those parts and set the sum equal to the goal of 50 mL.
\n" ); document.write( "1x+3x = 50
\n" ); document.write( "4x = 50
\n" ); document.write( "x = 50/4
\n" ); document.write( "x = 12.5\r
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\n" ); document.write( "\n" ); document.write( "She'll need x = 12.5 mL of one batch and 3x = 3*12.5 = 37.5 mL of the other batch.\r
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\n" ); document.write( "\n" ); document.write( "The question is: which values go where?\r
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\n" ); document.write( "\n" ); document.write( "Let's make a table where we have 12.5 mL of batch A and 37.5 mL of batch B
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	Amount of solution	Amount of pure morphine
A	12.5	0.10*12.5 = 1.25
B	37.5	0.50*37.5 = 18.75
Total	50	1.25+18.75 = 20

\n" ); document.write( "The takeaway from that table is we have 20 mL of pure morphine out of 50 mL total
\n" ); document.write( "20/50 = 0.40 = 40% is the final concentration.\r
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\n" ); document.write( "\n" ); document.write( "We wanted a 20% concentration instead, so we must flip the values.
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	Amount of solution	Amount of pure morphine
A	37.5	0.10*37.5 = 3.75
B	12.5	0.50*12.5 = 6.25
Total	50	3.75+6.25 = 10

\n" ); document.write( "10 mL of pure morphine out of 50 mL total
\n" ); document.write( "10/50 = 0.20 = 20% is the final concentration, which is the target we're after.\r
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\n" ); document.write( "\n" ); document.write( "Answers:
\n" ); document.write( "37.5 mL of the 10% solution
\n" ); document.write( "12.5 mL of the 50% solution\r
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\n" ); document.write( "\n" ); document.write( "More practice with a similar question
\n" ); document.write( "https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.1204463.html
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