document.write( "Question 768567: A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 5% active ingredient, but the pharmacist only has 20% solution and 2% solution in stock. How much of each type of solution should be used to fill the prescription? \n" ); document.write( "

Algebra.Com's Answer #468427 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ml of 20% solution needed
\n" ); document.write( "Let $\"+b+\"$ = ml of 2% solution needed
\n" ); document.write( "--------------
\n" ); document.write( "{1} $\"+a+%2B+b+=+15+\"$
\n" ); document.write( "(2) $\"+%28+.2a+%2B+.02b+%29+%2F+15+=+.05+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+.2a+%2B+.02b+=+.05%2A15+\"$
\n" ); document.write( "(2) $\"+.2a+%2B+.02b+=+.75+\"$
\n" ); document.write( "(2) $\"+20a+%2B+2b+=+75+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+20a+%2B+2b+=+75+\"$
\n" ); document.write( "(1) $\"+-2a+-+2b+=+-30+\"$
\n" ); document.write( " $\"+18a+=+45+\"$
\n" ); document.write( " $\"+a+=+2.5+\"$
\n" ); document.write( "and, since
\n" ); document.write( "{1} $\"+a+%2B+b+=+15+\"$
\n" ); document.write( "(1) $\"+b+=+15+-+2.5+\"$
\n" ); document.write( "(1) $\"+b+=+12.5+\"$
\n" ); document.write( "2.5 ml of 20% solution are needed
\n" ); document.write( "12.5 ml of 2% solution are needed
\n" ); document.write( "--------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.2a+%2B+.02b+%29+%2F+15+=+.05+\"$
\n" ); document.write( "(2) $\"+%28+.2%2A2.5+%2B+.02%2A12.5+%29+%2F+15+=+.05+\"$
\n" ); document.write( "(2) $\"+%28+.5+%2B+.25+%29+%2F+15+=+.05+\"$
\n" ); document.write( "(2) $\"+.75+=+.05%2A15+\"$
\n" ); document.write( "(2) $\"+.75+=+.75+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );