For this case he does not need anything of $ 124 / oz. Let's prove it.
Let
x = gold alloy required
(3-x) = silver alloy required
160x + 140 (3-x) = 438
160x + 420 - 140x = 438
160x - 140x = 438 - 420
20x = 18
x = 18/20
x = 0.9 oz gold alloy
3 - 0.9 = 2.1 oz silver alloy
We check the result:
0.9 (160) + 2.1 (140) =
144 + 294 = 438
answer:
No ounces of another alloy at $ 124 an ounce must she add to these in order to have a mixture of the three that she can use to make 3-ounce jewelry worth $ 438 a piece
