document.write( "Question 372765: A dehydrated patient needs a 2.6% saline IV. Unfortunately, the hospital only has bags of 8% and 2% saline solutions. How many liters of each solutions should be mixed together to yield 2 liters of the desired concentration. \n" ); document.write( "

Algebra.Com's Answer #265514 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = liters of 8% solution needed
\n" ); document.write( "Let $\"b\"$ = liters of 2% solution needed
\n" ); document.write( "In words:
\n" ); document.write( "(liters of saline)/(liters of solution) = 2.6%
\n" ); document.write( "(1) $\"%28.08a+%2B+.02b%29%2F2+=+.026\"$
\n" ); document.write( "(2) $\"a+%2B+b+=+2\"$
\n" ); document.write( "------------------
\n" ); document.write( "From (1):
\n" ); document.write( "(1) $\".08a+%2B+.02b+=+.052\"$
\n" ); document.write( "(1) $\"80a+%2B+20b+=+52\"$
\n" ); document.write( "Multiply both sides of (2) by $\"20\"$ and
\n" ); document.write( "subtract from (1)
\n" ); document.write( "(1) $\"80a+%2B+20b+=+52\"$
\n" ); document.write( "(2) $\"-20a+-+20b+=+-40\"$
\n" ); document.write( " $\"60a+=+12\"$
\n" ); document.write( " $\"a+=+.2\"$
\n" ); document.write( "And, since
\n" ); document.write( " $\"a+%2B+b+=+2\"$
\n" ); document.write( " $\"b+=+1.8\"$
\n" ); document.write( ".2 liters of 8% solution and 1.8 liters of 2% solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"%28.08a+%2B+.02b%29%2F2+=+.026\"$
\n" ); document.write( "(1) $\"%28.08%2A.2+%2B+.02%2A1.8%29%2F2+=+.026\"$
\n" ); document.write( "(1) $\"%28.016+%2B+.036%29%2F2+=+.026\"$
\n" ); document.write( " $\".052%2F2+=+.026\"$
\n" ); document.write( " $\".052+=+.052\"$
\n" ); document.write( "OK \n" ); document.write( "

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