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Question 170296This question is from textbook Introductory Algebra
: This is a story problem: 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?
Could you please lead me in the right direction for solving this problem?
This question is from textbook Introductory Algebra
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! This is a story problem: 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?
Could you please lead me in the right direction for solving this problem?
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In the first alloy, the gold is (3/4) of the alloy.
In the 2nd alloy, the gold is 5/12 of the alloy.
In the resulting alloy, 1/3 of 6 oz is gold, which is 4 oz.
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He can use x ounces of the 1st, and 6-x of the 2nd alloy.
So, x*(3/4) + (6-x)*(5/12) = 4
3x/4 + (6-x)*(5/12) = 4
Multiply by 12 to eliminate fractions
9x + 5*(6-x) = 48
9x + 30 -5x = 48
4x = 18
x = 4.5 (oz of the 1st alloy)
6-4.5 = 1.5 (oz of the 2nd alloy)
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