document.write( "Question 760543: A printer has ink that is 13% cobalt blue color and ink that is 17% cobalt blue color. How many ounces of each ink are needed to make 2 gallons (256 ounces) of ink that is 15% cobalt blue color \n" ); document.write( "

Algebra.Com's Answer #462724 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ounces of 13% ink needed
\n" ); document.write( "Let $\"+b+\"$ = ounces of 17% ink needed
\n" ); document.write( " $\"+.13a+\"$ = ounces of cobalt blue color in 13% ink
\n" ); document.write( " $\"+.17b+\"$ = ounces of cobalt blue color in 17% ink
\n" ); document.write( "---------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+256+\"$
\n" ); document.write( "(2) $\"+%28+.13a+%2B+.17b+%29+%2F+256+=+.15+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "(2) $\"+.13a+%2B+.17b+=+.15%2A256+\"$
\n" ); document.write( "(2) $\"+.13a+%2B+.17b+=+38.4+\"$
\n" ); document.write( "(2) $\"+13a+%2B+17b+=+3840+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+13+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+13a+%2B+17b+=+3840+\"$
\n" ); document.write( "(1) $\"+-13a+-+13b+=+-3328+\"$
\n" ); document.write( " $\"+4b+=+512+\"$
\n" ); document.write( " $\"+b+=+128+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+256+\"$
\n" ); document.write( "(1) $\"+a+%2B+128+=+256+\"$
\n" ); document.write( "(1) $\"+a+=+128+\"$
\n" ); document.write( "128 ounces of 13% ink are needed
\n" ); document.write( "128 ounces of 17% ink are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.13%2A128+%2B+.17%2A128+%29+%2F+256+=+.15+\"$
\n" ); document.write( "(2) $\"+%28+16.64+%2B+21.76+%29+%2F+256+=+.15+\"$
\n" ); document.write( "(2) $\"+38.4+=+.15%2A256+\"$
\n" ); document.write( "(2) $\"+38.4+=+38.4+\"$
\n" ); document.write( "OK \n" ); document.write( "

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