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 me

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Question 169573This question is from textbook Introductory Algebra
: 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? This question is from textbook Introductory Algebra

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the 3/4 gold alloy x and the 7/12 alloy y
:
x+y=6....eq 1
.75x+(7/12)y=2/3(6)...eq 2
x=6-y from eq 1 and plug it into eq 2
:
.75(6-y)+.4166y=4
:
4.5-.75y+.4166y=4
:
.3334y=.5
:
highlight%28y=1.5%29 oz of 7/12's alloy
highlight%28x=6-1.5=4.5%29oz of 3/4's alloy