Question 1020060: How much of an alloy that is 10% copper should be mixed with 400 ounces of an alloy that is 90% copper in order to get an outlier 30% copper Answer by LinnW(1048) (Show Source):
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Since we want 30% copper, we want 30 parts pure copper to 100 parts of the whole.
This is the right side of the above equation.
The numerator on the left hand side represents the total amount of pure
copper, that is 90% of the 400 ounces plus 10% of the alloy.
The denominator is the total amount of material in the new mixture.
Now we just need to solve.
Beginning with the cross products, we have
30(400+x) = 100(0.90(400)+0.10x)
12000 + 30x = 90(400) + 10x
12000 + 30x = 36000 + 10x
add -10x to each side
12000 + 20x = 36000
add -12000 to each side
20x = 24000
divide each side by 20
x = 1200
To verify, substitute 1200 for x in
This checks out, so we need 1200 ounces of the alloy.
