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 400 grams?
how many grams of 12-karat gold needs to be used to make the bracelet?

i need to be shown step by step please

Question

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 400 grams?
how many grams of 12-karat gold needs to be used to make the bracelet?

i need to be shown step by step please

kropot72 · Answer

Amount of gold in 14-carat 400 gram bracelet = 400 * 0.58 grams
Let x be the weight of 18-carat gold in the bracelet.
Let y be the weight of 12-carat gold in the bracelet.

x + y = 400 ..............................(1)
0.75x + 0.5y = 400 * 0.58 ........(2)

Now you need to solve the system of equations (1) and (2) to find the values of x and y.