Question 335632
Mass of Ag in final mixture = 6*2/3 = 4oz

Mass of 3/4 mixture required = x
Mass of 5/12 mixture required = y

Mass of Ag in final mixture = 4 = 3x/4 + 5y/12
Total mass of final mixture = 6 = x + y

48 = 9x + 5y
6 = x+y => x = 6-y

48 = 9(6-y) + 5y
48 = 54 - 9y + 5y
4y = 54-48 = 6
y = 6/4 = 3/2 ounce
x = 6-3/2 = 9/2 ounce

3/4 mixture = 9/2 = 4 1/2 ounce
5/12 mixture = 3/2 = 1 1/2 ounce

The goldsmith needs to use 4 1/2 ounce of the 3/4 mixture and 1 1/2 ounce of the 5/12 mixture to have 6 ounces of 2/3 mixture.