SOLUTION: I am absolutely baffled by this one. I am terrible at fractions anyway, but that to a word problem and I am lost. A goldsmith has two alloys that are different purities of gold

Question 183783: I am absolutely baffled by this one. I am terrible at fractions anyway, but that to a word problem and I am lost.
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 otain a 6 ounce mixture that is two-thirds pure gold?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 otain a 6 ounce mixture that is two-thirds pure gold?
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Equation:
gold + gold = gold
(3/4)x + (5/12)(6-x) = (2/3)*6
Multiply thru by 12 to get:
9x + 5(6-x) = 8*6
9x + 5*6 - 5x = 8*6
4x = 3*6
x = 9/2 = 4 1/2 oz (amt. of (3/4) pure gold in the mixture)
6-x = 6 - 4 1/2 = 1 1/2 oz (amt of (5/12) pure gold in the mixture)
========================================================
Cheers,
Stan H.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
In words:
(gold in the 3/4 alloy) + (gold in the 5/12 alloy) / (total amt of alloy)
= (gold in the final mixture)/(total amount of alloy)
Let = the ounces of 3/4 alloy needed
Let = the ounces of the 5/12 alloy needed
given:
Ounces of gold in 3/4 alloy =
Ounces of gold in the 5/12 alloy =
Ounces of alloy in the final mixture =
Ounces of gold in the final mixture =
--------------
(this is same as word description)
Multiply both sides by

Multiply both sides by

(1)
(2)
Subtract (1) from (2)
(2)
(1)

And, since

9/2 ounces of 3/4 alloy should be melted and mixed
with 3/2 ounces of 5/12 alloy
check answer:

Multiply both sides by

Multiply both sides by

OK

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