For thousands of years, gold has been considered one of the earth's most precious metals. one hundred percent pure gold is24-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 200 grams?

14 karat gold is 58.3333...% gold
We have 75% gold and 50% gold and we need to make 200 grams of 58.3333...% gold.

A) x + y = 200

B) .75x + .50y = ( (14/24) * 200)
We multiply equation B) by -1.3333... and get
B) -x -.6666...y = -155.5555... then adding A)
A) x + y = 200  we get

.3333...y = 44.4444...

y = 133.3333... grams 12 karat gold
x = 66.6666... grams  18 karat gold

Double-Checking the answer
133.3333... * .5 = 66.6666...
66.6666 * .75 = 50.0000...

Concentration of final solution = (66.6666... + 50) / 200 = 58.3333...% which is 14 karat gold