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
