document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162558>Question 1162558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A candy distributor needs to mix a 30% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 36% fat-content chocolate. How many kilograms of each kind of chocolate must they use? </SPAN>\n" );
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document.write( "Answer: <BR>\n" );
document.write( "<font color=red>80 kilograms</font> of the 30% fat content chocolate<BR>\n" );
document.write( "<font color=red>20 kilograms</font> of the 60% fat content chocolate\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "We have two kinds of chocolate, which we'll call A and B<BR>\n" );
document.write( "x = amount of chocolate A<BR>\n" );
document.write( "y = amount of chocolate B<BR>\n" );
document.write( "amounts are in kilograms<BR>\n" );
document.write( "x+y = total amount of chocolate from both candies<BR>\n" );
document.write( "x+y = 100, since we want 100 kg total<BR>\n" );
document.write( "y = -x+100, solve for y\r<BR>\n" );
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document.write( "0.30x = amount of pure fat from chocolate A<BR>\n" );
document.write( "0.60y = amount of pure fat from chocolate B<BR>\n" );
document.write( "0.30x+0.60y = total amount of pure fat from both chocolates combined<BR>\n" );
document.write( "0.30x+0.60y = 0.36*100<BR>\n" );
document.write( "0.30x+0.60y = 36<BR>\n" );
document.write( "the expression 0.36*100 represents 36% of the total amount 100 kg is pure fat. So we have 36 kg of pure fat\r<BR>\n" );
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document.write( "Plug in y = -x+100. Solve for x.<BR>\n" );
document.write( "0.30x+0.60y = 36<BR>\n" );
document.write( "0.30x+0.60( y ) = 36<BR>\n" );
document.write( "0.30x+0.60( -x+100 ) = 36 ... replace y with -x+100<BR>\n" );
document.write( "0.30x-0.60x+60 = 36 ... distribute<BR>\n" );
document.write( "-0.30x+60 = 36<BR>\n" );
document.write( "-0.30x = 36-60<BR>\n" );
document.write( "-0.30x = -24<BR>\n" );
document.write( "x = -24/(-0.30)<BR>\n" );
document.write( "x = 80\r<BR>\n" );
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document.write( "We can now find the value of y with this x value<BR>\n" );
document.write( "y = -x+100<BR>\n" );
document.write( "y = -80+100<BR>\n" );
document.write( "y = 20<BR>\n" );
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