document.write( "Question 323455: A 40% dye solution is to be mixed with a dye solution to get 120 liters of a 50% solution. How many liters of the 40% and 70% solutions will be needed? \n" ); document.write( "

Algebra.Com's Answer #231461 by josmiceli(19441) $\"\"$ $\"About$

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In words:
\n" ); document.write( "(final liters of dye)/(final liters of solution) = 50%
\n" ); document.write( "Let $\"a\"$ = liters of 40% solution needed
\n" ); document.write( "Let $\"b\"$ = liters of 70% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+%2B+b+=+120\"$
\n" ); document.write( "liters of dye in $\"a\"$ = $\".4a\"$
\n" ); document.write( "liters of dye in $\"b\"$ = $\".7b\"$
\n" ); document.write( "liters of dye in final solution = $\".5%2A120+=+60\"$
\n" ); document.write( "(2) $\".4a+%2B+.7b+=+60\"$
\n" ); document.write( "Multiply both sides of (1) by $\"4\"$
\n" ); document.write( "Multiply both sides of (2) by $\"10\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"4a+%2B+7b++=+600\"$
\n" ); document.write( "(1) $\"-4a+-+4b+=+-480\"$
\n" ); document.write( " $\"3b+=+120\"$
\n" ); document.write( " $\"b+=+40\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"a+%2B+b+=+120\"$
\n" ); document.write( " $\"a+=+120+-+40\"$
\n" ); document.write( " $\"a+=+80\"$
\n" ); document.write( "80 liters of 40% solution and 40 liters of 70% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\".4a+%2B+.7b+=+60\"$
\n" ); document.write( "(2) $\".4%2A80+%2B+.7%2A40+=+60\"$
\n" ); document.write( " $\"32+%2B+28+=+60\"$
\n" ); document.write( " $\"60+=+60\"$
\n" ); document.write( "OK \n" ); document.write( "

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