document.write( "Question 815060: thank you for helping math
\n" ); document.write( "Allegation Problem: Word Problem \r
\n" ); document.write( "\n" ); document.write( "In what proportion must plain coal tar be combined with a 2% coal tar ointment to make a 4% coal tar ointment?\r
\n" ); document.write( "\n" ); document.write( "thank you again. \n" ); document.write( "

Algebra.Com's Answer #490690 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
2% is $\"+2%2F100+=+.02+\"$
\n" ); document.write( "4% is $\"+4%2F100+=+.04+\"$
\n" ); document.write( "Plain coal tar is 100% = $\"+100%2F100+=+1+\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( "Let $\"+a\"$ = units of 2% coal tar needed
\n" ); document.write( "Let $\"+b+\"$ = units of 100% coal tar needed
\n" ); document.write( "( I will choose units for $\"a\"$ and $\"b\"$
\n" ); document.write( "so that $\"a+%2B+b+=+10+\"$ units
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "(1) $\"+%28+.02a+%2B+1%2Ab+%29+%2F+%28+a+%2B+b+%29+=+.04+\"$
\n" ); document.write( "(2) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( "---------------
\n" ); document.write( "(1) $\"+.02a+%2B+b+=+.04%2A%28+a+%2B+b+%29+\"$
\n" ); document.write( "(1) $\"+.02a+%2B+b+=+.04a+%2B+.04b+%29+\"$
\n" ); document.write( "(1) $\"+.96b+-+.02a+=+0+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+a+=+10+-+b+\"$
\n" ); document.write( "by substitution:
\n" ); document.write( "(1) $\"+.96b+-.02%2A%28+10+-+b+%29+=+0+%29+\"$
\n" ); document.write( "(1) $\"+.96b+-+.2+%2B+.02b+=+0+\"$
\n" ); document.write( "(1) $\"+.98b+=+.2+\"$
\n" ); document.write( "(1) $\"+b+=+10%2F49+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+a+=+10+-+b+\"$
\n" ); document.write( "(2) $\"+a+=+10+-+10%2F49+\"$
\n" ); document.write( "(2) $\"+a+=+490%2F49+-+10%2F49+\"$
\n" ); document.write( "(2) $\"+a+=+480%2F49+\"$
\n" ); document.write( "------------------
\n" ); document.write( "The proportion of plain coal tar to 2% coal tar
\n" ); document.write( "should be:
\n" ); document.write( " $\"+b%2Fa+=+%28+1%2F49+%29+%2F+%28+480%2F49+%29+\"$
\n" ); document.write( " $\"+b%2Fa+=+1%2F480++\"$
\n" ); document.write( "--------------
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+%28+.02a+%2B+1%2Ab+%29+%2F+10+=+.04+\"$
\n" ); document.write( "(1) $\"++.02a+%2B+b++=+.4+\"$
\n" ); document.write( "(1) $\"+.02a+=+.4+-+b+\"$
\n" ); document.write( "(1) $\"+.02%2A%28+480%2F49+%29+=+.4+-+10%2F49+\"$
\n" ); document.write( "Multiply both sides by $\"+49+\"$
\n" ); document.write( "(1) $\"+.02%2A480+=+.4%2A49+-+10+\"$
\n" ); document.write( "(1) $\"+9.6+=+19.6+-+10+\"$
\n" ); document.write( "(1) $\"+9.6+=+9.6+\"$
\n" ); document.write( "OK \n" ); document.write( "

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