document.write( "Question 399532: A pharmacist is to prepare 18 milliliters of special eye drops for a
\n" ); document.write( "glaucoma patient. The eye-drop solution must have a 3% active ingredient,
\n" ); document.write( "but the pharmacist only has 9% solution and 2% solution in stock. How
\n" ); document.write( "much of each type of solution should be used to fill the prescription? \n" ); document.write( "

Algebra.Com's Answer #282914 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
In words:
\n" ); document.write( "(ml of active ingredient)/(ml of total solution) = 3%
\n" ); document.write( "Let $\"a\"$ = ml of 9% solution to use
\n" ); document.write( "Let $\"b\"$ = ml of 2% solution to use
\n" ); document.write( "-----------------
\n" ); document.write( "given:
\n" ); document.write( " $\".09a\"$ = ml of active ingredient in 9% solution
\n" ); document.write( " $\".02b\"$ = ml of active ingredient in 2% solution
\n" ); document.write( "(1) $\"a+%2B+b+=+18\"$ ml
\n" ); document.write( "--------------------
\n" ); document.write( "(2) $\"%28.09a+%2B+.02b%29%2F+18+=+.03\"$
\n" ); document.write( "(2) $\".09a+%2B+.02b+=+.54\"$
\n" ); document.write( "(2) $\"9a+%2B+2b+=+54\"$
\n" ); document.write( "Multiply both sides of (1) by $\"2\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"9a+%2B+2b+=+54\"$
\n" ); document.write( "(1) $\"-2a+-+2b+=+-36\"$
\n" ); document.write( " $\"7a+=+18\"$
\n" ); document.write( " $\"a+=+18%2F7\"$ ml
\n" ); document.write( "and, from (1)
\n" ); document.write( "(1) $\"a+%2B+b+=+18\"$
\n" ); document.write( " $\"b+=+18+-+18%2F7\"$
\n" ); document.write( " $\"b+=+%28126+-+18%29%2F7\"$
\n" ); document.write( " $\"b+=+108%2F7\"$ ml
\n" ); document.write( "18/7 ml of 9% solution must be used
\n" ); document.write( "108/7 ml of 2% solution must be used
\n" ); document.write( "-------------------------------------
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"%28.09a+%2B+.02b%29%2F+18+=+.03\"$
\n" ); document.write( "(2) $\"%28.09%2A%2818%2F7%29+%2B+.02%2A%28108%2F7%29%29%2F+18+=+.03\"$
\n" ); document.write( "(2) $\"%289%2A%2818%2F700%29+%2B+2%2A%28108%2F700%29%29%2F+18+=+3%2F100\"$
\n" ); document.write( "(2) $\"%289%2A%2818%2F700%29+%2B+2%2A%28108%2F700%29%29%2F+18+=+21%2F700\"$
\n" ); document.write( "(2) $\"162+%2B+216+=+18%2A21\"$
\n" ); document.write( "(2) $\"378+=+378\"$
\n" ); document.write( "OK \r
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