SOLUTION: For thousands of​ years, gold has been considered one of the​ Earth's most precious metals. One hundred percent pure gold is​ 24-karat gold, which is too soft to

Algebra ->  Linear-equations -> SOLUTION: For thousands of​ years, gold has been considered one of the​ Earth's most precious metals. One hundred percent pure gold is​ 24-karat gold, which is too soft to       Log On


   



Question 1124264: For thousands of​ years, gold has been considered one of the​ Earth's most precious metals. One hundred percent pure gold is​ 24-karat gold, which is too soft to be made into jewelry. Most gold jewelry is​ 14-karat gold, approximately​ 58% gold. If​ 18-karat gold is​ 75% gold and​ 12-karat gold is​ 50% gold, how much of each should be used to make a​ 14-karat gold bracelet weighing 50 ​grams?
How many grams of​ 18-karat gold needs to be used to make the​ bracelet?
? grams
How many grams of​ 12-karat gold needs to be used to make the​ bracelet?
? grams

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = grams of 12 karat gold needed
Let +b+ = grams of 18 karat gold needed
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(1) +a+%2B+b+=+50+
(2) +%28+.5a+%2B+.75b+%29+%2F+50+=+.58+
覧覧覧覧覧覧覧覧-
(2) +.5a+%2B+.75b+=+29+
Multiply both sides by +2+ and
Subtract (1) from (2)
(2) +a+%2B+1.5b+=+58+
(1) +-a+-+b+=+50+
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+.5b+=+8+
+b+=+16+
And
(1) +a+%2B+16+=+50+
(1) +a+=+34+
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34 g of 12 k gold
16 g of 18 k gold