Question

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?

Answer 1

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

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