document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196993>Question 1196993</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A clothing manufacturer has some pure silk thread and some thread that is 80% silk. How many kilograms of each must be woven together to make 60 kg of cloth that is 95% silk? \r<BR>\n" );
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document.write( "pure silk thread=__________ HOW Much KG?  	<BR>\n" );
document.write( "80% silk thread= _________ HOW Much KG?   	 </SPAN>\n" );
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document.write( "I'll label the threads A,B,C<BR>\n" );
document.write( "Thread A = pure silk, aka 100% silk<BR>\n" );
document.write( "Thread B = 80% silk thread<BR>\n" );
document.write( "Thread C = 95% silk\r<BR>\n" );
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document.write( "The clothing manufacturer has thread A and thread B, but they don't have thread C.<BR>\n" );
document.write( "The goal is to somehow mix the two given threads (A & B) to get thread C.\r<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "x = amount of thread A, in kg<BR>\n" );
document.write( "Since we want 60 kg of thread C, this means 60-x represents the amount of thread B in kg.<BR>\n" );
document.write( "The expressions x and 60-x add to 60.\r<BR>\n" );
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document.write( "Thread A is pure silk, so we have x kilograms of pure silk so far.<BR>\n" );
document.write( "Thread B is 80% silk, which means we contribute another 0.80(60-x) = 48-0.80x kilograms of pure silk onto the x already there.\r<BR>\n" );
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document.write( "A+B = (x)+(48-0.80x) = 48+0.20x = total amount of pure silk.\r<BR>\n" );
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document.write( "Divide this over the 60 kg of total fabric, and we want this ratio to be 0.95 due to the 95% target rate.\r<BR>\n" );
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document.write( "(amount of pure silk)/(amount of fabric total) = 95% silk<BR>\n" );
document.write( "(48+0.20x)/(60) = 0.95\r<BR>\n" );
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document.write( "Let's solve for x.<BR>\n" );
document.write( "(48+0.20x)/60 = 0.95<BR>\n" );
document.write( "48+0.20x = 60*0.95<BR>\n" );
document.write( "48+0.20x = 57<BR>\n" );
document.write( "0.20x = 57-48<BR>\n" );
document.write( "0.20x = 9<BR>\n" );
document.write( "x = 9/0.2<BR>\n" );
document.write( "x = 45<BR>\n" );
document.write( "We need 45 kg of thread A (the pure 100% silk)<BR>\n" );
document.write( "and we need 60-x = 60-45 = 15 kg of thread B (the 80% silk)\r<BR>\n" );
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document.write( "100% of 45 = 45 kg of pure silk is from thread A<BR>\n" );
document.write( "80% of 15 = 0.8*15 = 12 kg of pure silk is from thread B<BR>\n" );
document.write( "We get 45+12 = 57 kg of pure silk out of 60 kg total<BR>\n" );
document.write( "57/60 = 0.95 = 95% so we've reached the proper target.\r<BR>\n" );
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document.write( "<font color=red>Answers</font><BR>\n" );
document.write( "pure silk thread = <font color=red>45 kg</font><BR>\n" );
document.write( "80% silk thread = <font color=red>15 kg</font>\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "The target is 95%<BR>\n" );
document.write( "The gap from 100% to 95% is 5 percentage points<BR>\n" );
document.write( "The gap from 80% to 95% is 15 percentage points\r<BR>\n" );
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document.write( "We write the results in reverse order to get the ratio 15:5 which reduces to 3:1<BR>\n" );
document.write( "This tells us we need 3 times as much of the pure silk compared to the 80% silk<BR>\n" );
document.write( "This is because the 3 is listed first and the pure silk is listed first.\r<BR>\n" );
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document.write( "n = some unknown positive real number<BR>\n" );
document.write( "The ratio 3:1 scales up to 3n:1n<BR>\n" );
document.write( "These two parts must add to 60 kg total<BR>\n" );
document.write( "3n+1n = 60<BR>\n" );
document.write( "4n = 60<BR>\n" );
document.write( "n = 60/4<BR>\n" );
document.write( "n = 15<BR>\n" );
document.write( "We need 3n = 3*15 = 45 kg of the pure silk and 1n = 1*15 = 15 kg of the 80% silk\r<BR>\n" );
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document.write( "<font color=red>Answers</font><BR>\n" );
document.write( "pure silk thread = <font color=red>45 kg</font><BR>\n" );
document.write( "80% silk thread = <font color=red>15 kg</font><BR>\n" );
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