Question

A metallurgist has one alloy containing 22% copper and another containing 53% copper. How many pounds of each alloy must he use to make 51 pounds of a third alloy containing 30% copper? (Round to two decimal places if necessary.)

Answer 1

37.8387 pounds of the 22% alloy copper and 13.1612 pounds of the 53% alloy copper must be used.

Explanation:

Let x represent the amount of 22% copper needed.

Therefore, 51-x represents the amount of 53% copper needed.

Therefore, we can write

(22% * x) + (53% * (51-x)) = 30% * (51)

⇒0.22x + 0.53(51-x) = 0.3(51)

⇒ x = 37.8387

Thus, x =37.8387 and 51-x = 13.1612