Question

Mixture question please help!! (will give brainliest to an answer with step-by-step)

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 250 grams?

Answer 1

Answer:

83.3 g of 18-karat gold and 166.7 g of 12-karat gold

Step-by-step explanation:

24-karat gold is pure gold. The purity is 24/24 = 1 = 100% gold.

12-karat gold is 50% gold. The purity is 12/24 = 0.5 = 50% gold.

14-karat gold is 14/24 pure, so in 250 g of 14-karat gold the amount of pure gold is

14/24 * 250 g

The total weight of the bracelet is 250 g.

Let x = the weight of 18-karat gold.

Then the weight of 14-karat gold needed is 250 - x.

weight of pure gold from 14-karat gold + weight of pure gold from 18-karat gold = weight of pure gold in 14-karat gold bracelet

0.5 * (250 - x) + 0.75x = 14/24 * 250

125 - 0.5x + 0.75x = 7/12 * 250

125 + 0.25x = 7/12 * 250

1500 + 3x = 1750

3x = 250

x = 250/3

x = 83.3

250 - x = 250 - 83.3 = 166.7

Answer: 83.3 g of 18-karat gold and 166.7 g of 12-karat gold