SOLUTION: A metallurgist needs to make 12.4 lb. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of e

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Question 188966: A metallurgist needs to make 12.4 lb. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should be used?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let x and y be the amounts of 60% and 40% gold respectively
:
x+y=12.4...........eq 1
.6x+.4y=.5(12.4)...eq 2
:
rewrite eq 1 to x=12.4-y and plug into eq 2
:
.6(12.4-y)+.4y=6.2
:
7.44-.6y+.4y=6.2
:
-.2y=-1.24
:
y=6.2 pounds of 40% gold
:
x=12.4-6.2=6.2 pounds of 60% gold
:
equal proportions makes perfect sense....since 50% is right in the middle of 40% and 60%