document.write( "Question 784649: What quantity of a 55% acid solution must be mixed with a 45% solution to produce 600 mL of a 50% solution? \n" ); document.write( "

Algebra.Com's Answer #477183 by josgarithmetic(39618) $\"\"$ $\"About$

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ASSIGN VARIABLES TO ALL QUANTITIES
\n" ); document.write( "L, the lower concentration of available material, 45%
\n" ); document.write( "H, the higher concentration of available material, 55%
\n" ); document.write( "T, the target concentration of resulting mixture, 50%
\n" ); document.write( "M, the amount of resulting mixture, 600 ml.
\n" ); document.write( "x, the amount of lower concentrated material to use, unknown
\n" ); document.write( "y, the amount of higher concentrated material to use, unknown\r
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\n" ); document.write( "\n" ); document.write( "EQUATION \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28%28Lx%2ByH%29%2FM=T%29\"$ and $\"highlight%28x%2By=M%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28Lx%2ByH%29%2FM=T\"$
\n" ); document.write( " $\"Lx%2ByH=TM\"$
\n" ); document.write( " $\"Lx%2B%28M-x%29H=TM\"$
\n" ); document.write( " $\"Lx%2BHM-Hx=TM\"$
\n" ); document.write( " $\"%28L-H%29x%2BHM=TM\"$
\n" ); document.write( " $\"%28L-H%29x=TM-HM\"$
\n" ); document.write( " $\"%28L-H%29x=%28T-H%29M\"$
\n" ); document.write( " $\"x=M%28T-H%29%2F%28L-H%29\"$ , and since the two differences here would both be negative,
\n" ); document.write( "we can multiply by (-1)/(-1),
\n" ); document.write( " $\"highlight%28x=M%28H-T%29%2F%28H-L%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "After using that formula, you can simply use $\"highlight%28y=M-x%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Substitute the necessary values and compute x and y. \n" ); document.write( "

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