document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170861>Question 1170861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello i need ASAP help can someone please answer <BR>\n" );
document.write( "Steve is a jeweller who wants to create rings of a certain gold purity. 24-kt (karat) is considered<BR>\n" );
document.write( "pure gold. Steve has a stock of 18-kt and 10-kt on hand. He wants to have 200g of 16-kt gold. How much<BR>\n" );
document.write( "18-kt and 10-kt does he need to have a 200g sample? <BR>\n" );
document.write( "thank you  </SPAN>\n" );
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document.write( "kt = karat<BR>\n" );
document.write( "24 kt = 100% pure gold<BR>\n" );
document.write( "18 kt = (18/24)*100% = (0.75)*100% = 75%<BR>\n" );
document.write( "This indicates the 18 kt stock is 75% pure gold\r<BR>\n" );
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document.write( "Similarly,<BR>\n" );
document.write( "10 kt = (10/24)*100% = (0.41667)*100% = 41.667%<BR>\n" );
document.write( "The 10 kt stock is roughly 41.667% pure gold.\r<BR>\n" );
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document.write( "And,<BR>\n" );
document.write( "16 kt = (16/24)*100% = 66.667%<BR>\n" );
document.write( "The 16 kt stock is roughly 66.667% pure gold\r<BR>\n" );
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document.write( "I'll use the fractional form of each decimal value to avoid rounding errors.\r<BR>\n" );
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document.write( "In other words,<BR>\n" );
document.write( "18 kt = (18/24) of pure gold = (3/4) of pure gold<BR>\n" );
document.write( "10 kt = (10/24) of pure gold = (5/12) of pure gold<BR>\n" );
document.write( "16 kt = (16/24) of pure gold = (2/3) of pure gold\r<BR>\n" );
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document.write( "Fractions can be a pain to work with, but they provide exact values.\r<BR>\n" );
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document.write( "Let <BR>\n" );
document.write( "x = amount of the 18 kt gold stock<BR>\n" );
document.write( "y = amount of the 10 kt gold stock<BR>\n" );
document.write( "amounts are in grams\r<BR>\n" );
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document.write( "If steve has x grams of 18 kt gold, then he has (3/4)x grams of pure gold. Recall that in the previous section 3/4 = 75% was the amount of pure gold from this stock. Effectively we have (3/4)x grams of pure gold (24 kt gold) mixed in with some other metal, likely copper or iron perhaps. This means the other 1/4 is the other metal.\r<BR>\n" );
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document.write( "If steve has y grams of 10 kt gold, then he has (10/24)y grams of pure gold. The fraction 10/24 reduces to 5/12. So (10/24)y = (5/12)y\r<BR>\n" );
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document.write( "The two amounts of pure gold add to <BR>\n" );
document.write( "(3/4)x+(5/12)y\r<BR>\n" );
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document.write( "Steve wants to have 200 grams of 16 kt gold, so he wants 200*(2/3) = 400/3 grams of pure gold.<BR>\n" );
document.write( "The 2/3 is from reducing 16/24.\r<BR>\n" );
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document.write( "Set the result 400/3 equal to the previous sum we got, and we end up with this equation<BR>\n" );
document.write( "(3/4)x+(5/12)y = 400/3<BR>\n" );
document.write( "This equation represents summing the pure gold amounts of each stock, getting a final amount of pure gold for the mixture. \r<BR>\n" );
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document.write( "To make life easier, multiply both sides by the LCD 12 to clear out the fractions<BR>\n" );
document.write( "(3/4)x+(5/12)y = 400/3<BR>\n" );
document.write( "12 * [(3/4)x+(5/12)y] = 12*400/3<BR>\n" );
document.write( "9x+5y = 1600<BR>\n" );
document.write( "Now everything is a whole number which is fairly nice.\r<BR>\n" );
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document.write( "Since he wants the final amount to be 200 grams, this must mean the subtotals of x and y have to add to 200\r<BR>\n" );
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document.write( "We can then solve for y getting<BR>\n" );
document.write( "x+y = 200<BR>\n" );
document.write( "x+y-x = 200-x<BR>\n" );
document.write( "y = 200-x\r<BR>\n" );
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document.write( "Plug this into the equation we found at the conclusion of the last section. Then solve for x.<BR>\n" );
document.write( "9x+5y = 1600<BR>\n" );
document.write( "9x+5(y) = 1600<BR>\n" );
document.write( "9x+5(200-x) = 1600<BR>\n" );
document.write( "9x+1000-5x = 1600<BR>\n" );
document.write( "4x+1000 = 1600<BR>\n" );
document.write( "4x+1000-1000 = 1600-1000<BR>\n" );
document.write( "4x = 600<BR>\n" );
document.write( "4x/4 = 600/4<BR>\n" );
document.write( "x = 150\r<BR>\n" );
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document.write( "He needs 150 grams of the 18 kt gold stock.\r<BR>\n" );
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document.write( "Use this to find y<BR>\n" );
document.write( "y = 200-x<BR>\n" );
document.write( "y = 200-150<BR>\n" );
document.write( "y = 50\r<BR>\n" );
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document.write( "He needs 50 grams of the 10 kt gold stock\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "150 grams of the 18 kt gold stock.<BR>\n" );
document.write( "50 grams of the 10 kt gold stock.\r<BR>\n" );
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