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

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Question 129650This question is from textbook Introductory Algebra
: A goldsmith has two alloys that are different purities of gold. The first is three-fourthspure 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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a= the amount of the 1st alloy used in ounces
Let b= the amount of the 2nd alloy used in ounces
%28%283%2F4%29%2Aa+%2B+%285%2F12%29%2Ab%29+%2F+6+=+2%2F3
a+%2B+b+=+6
b+=+6+-+a
%28%283%2F4%29%2Aa+%2B+%285%2F12%29%286+-+a%29%29+%2F+6+=+2%2F3
multiply both sides by 6
%283%2F4%29%2Aa+%2B+%285%2F12%29%286+-+a%29+=+12%2F3
multiply both sides by 12
9a+%2B+30+-+5a+=+48
4a+=+18
a+=+4.5
b+=+6+-+a
b+=+1.5
Use 4.5 oz of the 3/4 gold and 1.5 oz of the 5/12 gold
check
%28%283%2F4%29%2Aa+%2B+%285%2F12%29%2Ab%29+%2F+6+=+2%2F3
%28.75%2A4.5+%2B+.4167%2A1.5%29+%2F+6+=+.6667
%283.375+%2B+.6251%29+%2F+6+=+.6667
4.0001+%2F+6+=+.6667
.66668+=+.6667
close enough