A goldsmith has two alloys that are different purities of gold. The first is 3/4 pure gold and the second is?

5/12 pure gold. How many ounces of each should be melted and mixed in order to obtain a 6oz mixture that is 2/3 pure gold?

(3/4)x + (5/12)(6 – x) = 6(2/3)

=> 9x/12 + (5/2) – 5x/12 = 4
=> 4x/12 = 4 – 5/2
=> x/3 = 3/2
=> x = 9/2

So you need 9/2 (4.5) oz of the 3/4 pure gold and 1.5 oz of the 5/12 pure gold.

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