SOLUTION: A goldsmith has two alloys that are different purities of gold. The first is three-fourths pure gold and the second is five-twelfths pure gold. How many ounces of each should be

Question 274930:
A goldsmith has two alloys that are different purities of gold. The first is three-fourths pure gold and the second is five-twelfths pure gold. How many ounces of each should be melted and mixed in order to obtain a 6-oz mixture that is two-thirds pure gold?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
3/4x+5/12(6-x)=2/3*6
3x/4+30/12-5x/12=12/3
3x/4+2.5-5x/12=4
3x/4-5x/12=4-2.5
(3x*3-5x)/12=1.5
(9x-5x)/12=1.5
4x/12=1.5
x/3=1.5
x=4.5 oz. of the 3/4 pure gold is needed.
6-4.5=1.5 oz. of the 5/12 pure gold is needed.
Proof:
3/4*4.5+5/12*1.5=2/3*6
13.5/4+7.5/12=4
3.375+.625=4
4=4

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