document.write( "Question 279858: A 10% salt solution is mixed with an 18% salt solution to obtain a 32 oz 15% solution. How many ounces of each are needed? \n" ); document.write( "

Algebra.Com's Answer #203402 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = ounces of 10% solution needed
\n" ); document.write( "Let $\"b\"$ = ounces of 18% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+%2B+b+=+32\"$ ounces
\n" ); document.write( "(2) $\".1a+%2B+.18b+=+.15%2A32\"$
\n" ); document.write( "(2) $\".1a+%2B+.18b+=+4.8\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Multiply both sides of (2) by $\"100\"$
\n" ); document.write( "(2) $\"10a+%2B+18b+=+480\"$
\n" ); document.write( "Multiply both sides of (1) by $\"10\"$
\n" ); document.write( "and subtract from (2)
\n" ); document.write( "(2) $\"10a+%2B+18b+=+480\"$
\n" ); document.write( "(1) $\"-10a+-+10b+=+-320\"$
\n" ); document.write( " $\"8b+=+160\"$
\n" ); document.write( " $\"b+=+20\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"a+%2B+b+=+32\"$
\n" ); document.write( " $\"a+%2B+20+=+32\"$
\n" ); document.write( " $\"a+=+12\"$
\n" ); document.write( "12 ounces of 10% solution and 20 ounces of 18% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\".1a+%2B+.18b+=+4.8\"$
\n" ); document.write( " $\".1%2A12+%2B+.18%2A20+=+4.8\"$
\n" ); document.write( " $\"1.2+%2B+3.6+=+4.8\"$
\n" ); document.write( " $\"4.8+=+4.8\"$
\n" ); document.write( "OK \n" ); document.write( "

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