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 350 grams?

112 mg of 18-karat gold and  238 mg of 14-karat gold

Step-by-step explanation:

Let's call m1 the mass of 18-karat gold, and m2 the mass of 12-karat gold. They will be used to form 350 mg of 14-karat gold, so:

m1 + m2 = 350

m2 = 350 - m1 (equation 1)

For a mass balance of gold, the gold in 18-karat gold(75% of m1) plus the gold in 12-karat gold (50% of m2) must be equal to the gold in the 14-karat gold (58% of 350):

0.75m1 + 0.50m2 = 0.58x350

0.75m1 + 0.50m2 = 203

Replacing equation 1:

0.75m1 + 0.50x(350 - m1) = 203

0.75m1 + 175 - 0.5m1 = 203

0.25m1 = 28

m1 = 112 mg of 18-karat gold

m2 = 350 - 112

m2 = 238 mg of 14-karat gold

5050

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