SOLUTION: A goldsmith has teo alloys that are different purities of gold. The first three-fourths pure gold and the second is five-twelfths pure gold. How many ounces of each should be melte
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Question 335334: A goldsmith has teo alloys that are different purities of gold. The first 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-ounce mixture that is two-thirds pure gold?
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
Mass of Ag in final mixture = 6*2/3 = 4oz
Mass of 3/4 mixture required = x
Mass of 5/12 mixture required = y
Mass of Ag in final mixture = 4 = 3x/4 + 5y/12
Total mass of final mixture = 6 = x + y
48 = 9x + 5y
6 = x+y => x = 6-y
48 = 9(6-y) + 5y
48 = 54 - 9y + 5y
4y = 54-48 = 6
y = 6/4 = 3/2 ounce
x = 6-3/2 = 9/2 ounce
3/4 mixture = 9/2 = 4 1/2 ounce
5/12 mixture = 3/2 = 1 1/2 ounce
The goldsmith needs to use 4 1/2 ounce of the 3/4 mixture and 1 1/2 ounce of the 5/12 mixture to have 6 ounces of 2/3 mixture.
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