document.write( "Question 687734: The Royal Fruit Company produces two types of fruit drinks. The first type is 50% pure fruit juice, and the second type is 75% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice? \n" ); document.write( "

Algebra.Com's Answer #425329 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = pints of 50% pure fruit juice needed
\n" ); document.write( "Let $\"+b+\"$ = pints of 75% pure fruit juice needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.75b+%29+%2F+50+=+.65+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+.5a+%2B+.75b+=+.65%2A50+\"$
\n" ); document.write( "(2) $\"+.5a+%2B+.75b+=+32.5+\"$
\n" ); document.write( "(2) $\"+50a+%2B+75b+=+3250+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+50+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+50a+%2B+75b+=+3250+\"$
\n" ); document.write( "(1) $\"+-50a+-+50b+=+-2500+\"$
\n" ); document.write( " $\"+25b+=+750+\"$
\n" ); document.write( " $\"+b+=+30+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+a+=+50+-+b+\"$
\n" ); document.write( "(1) $\"+a+=+50+-+30+\"$
\n" ); document.write( "(1) $\"+a+=+20+\"$
\n" ); document.write( "20 pints of 50% pure fruit juice are needed
\n" ); document.write( "30 pints of 75% pure fruit juice are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.75b+%29+%2F+50+=+.65+\"$
\n" ); document.write( "(2) $\"+%28+.5%2A20+%2B+.75%2A30+%29+%2F+50+=+.65+\"$
\n" ); document.write( "(2) $\"+%28+10+%2B+22.5+%29+%2F+50+=+.65+\"$
\n" ); document.write( "(2) $\"+32.5%2F50+=+.65+\"$
\n" ); document.write( "(2) $\"+32.5+=+.65%2A50+\"$
\n" ); document.write( "(2) $\"+32.5+=+32.5+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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