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 200 grams?

Question

Mathematics

Aryanna Hopkins

2 September, 21:18

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 200 grams?

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Answers (1)

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Cornelius Fletcher · Answer 1

14 karat gold is 58.3333 ... % gold

We have 75% gold and 50% gold and we need to make 200 grams of 58.3333 ... % gold.

A) x + y = 200

B).75x +.50y = ((14/24) * 200)

We multiply equation B) by - 1.3333 ... and get

B) - x -.6666 ... y = - 155.5555 ... then adding A)

A) x + y = 200 we get

.3333 ... y = 44.4444 ...

y = 133.3333 ... grams 12 karat gold

x = 66.6666 ... grams 18 karat gold

Double-Checking the answer

133.3333 ... *.5 = 66.6666 ...

66.6666 *.75 = 50.0000 ...

Concentration of final solution = (66.6666 ... + 50) / 200 = 58.3333 ... % which is 14 karat gold