document.write( "Question 349169: Pure acid is to be added to a 5% acid solution to obtain 95L if 80% solution. What amounts of each should be used? \n" ); document.write( "

Algebra.Com's Answer #249616 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ liters = amount of pure acid to be added
\n" ); document.write( "Let $\"b\"$ liters = amount of 5% solution needed
\n" ); document.write( "In words:
\n" ); document.write( "(total liters of acid in final solution)/(total liters of final solution)
\n" ); document.write( "= 80%
\n" ); document.write( "----------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+%2B+b+=+95\"$
\n" ); document.write( " $\"%28a+%2B+.05b%29%2F95+=+.8\"$
\n" ); document.write( " $\"a+%2B+.05b+=+76\"$
\n" ); document.write( "(2) $\"100a+%2B+5b+=+7600\"$
\n" ); document.write( "Multiply both sides of (1) by $\"5\"$ and
\n" ); document.write( "subtract from (2)
\n" ); document.write( "(2) $\"100a+%2B+5b+=+7600\"$
\n" ); document.write( "(1) $\"-5a+-+5b+=+-475\"$
\n" ); document.write( " $\"95a+=+7125\"$
\n" ); document.write( " $\"a+=+75\"$
\n" ); document.write( " $\"b+=+95+-+75\"$
\n" ); document.write( " $\"b+=+20\"$
\n" ); document.write( "75 liters of pure acid and 20 liters of 5% acid solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( " $\"%28a+%2B+.05b%29%2F95+=+.8\"$
\n" ); document.write( " $\"%2875+%2B+.05%2A20%29%2F95+=+.8\"$
\n" ); document.write( " $\"%2875+%2B+1%29%2F95+=+.8\"$
\n" ); document.write( " $\"76%2F95+=+.8\"$
\n" ); document.write( " $\"76+=+76\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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