document.write( "Question 1115859: A plant food is to be made from three chemicals. The combined amounts of the first two chemicals must be 70% of the resulting mix. The second and third chemicals must be in the ratio of 4 to 3 by weight. How much of each chemical is needed to make 700 kg of the plant food? \n" ); document.write( "

Algebra.Com's Answer #730689 by josgarithmetic(39620) $\"\"$ $\"About$

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First, second, and third ingredients
\n" ); document.write( "x, y, z\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x%2By%29%2F700=0.7\"$
\n" ); document.write( " $\"x%2By=700%2A0.7\"$
\n" ); document.write( " $\"x%2By=7%2A7%2A100%2A0.1\"$
\n" ); document.write( " $\"x%2By=49%2A10\"$
\n" ); document.write( " $\"x%2By=490\"$
\n" ); document.write( "-
\n" ); document.write( " $\"y%2Fz=4%2F3\"$
\n" ); document.write( "-
\n" ); document.write( " $\"x%2By%2Bz=700\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-\r
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\n" ); document.write( "\n" ); document.write( "The three equations from the description are:
\n" ); document.write( " $\"system%28x%2By%2Bz=700%2Cx%2By=490%2C3y=4z%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note that the expression $\"x%2By\"$ occurs twice in the list of equations.\r
\n" ); document.write( "\n" ); document.write( " $\"system%28%28x%2By%29%2Bz=700%2Cx%2By=490%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Subtract the corresponding members to find $\"z=700-490\"$
\n" ); document.write( " $\"highlight%28z=210%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3y=4z\"$
\n" ); document.write( " $\"y=4z%2F3\"$
\n" ); document.write( " $\"y=4%2A210%2F3\"$
\n" ); document.write( " $\"y=4%2A70\"$
\n" ); document.write( " $\"highlight%28y=280%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2By=490\"$
\n" ); document.write( " $\"x=490-y\"$
\n" ); document.write( " $\"x=490-280\"$
\n" ); document.write( " $\"highlight%28x=210%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "-----------------------------------
\n" ); document.write( "

\r\n" );
document.write( "    MATERIAL           KILOGRAMS\r\n" );
document.write( "x   first chemical      210\r\n" );
document.write( "y   second chemical     280\r\n" );
document.write( "z   third chemical      210\r\n" );
document.write( "

\n" ); document.write( "------------------------------------ \n" ); document.write( "

\n" );