Q:

# A metallurgist has one alloy containing 34% copper another containing 48% copper. How many pounds of each alloy must he use to make 46 pounds of the third alloy containing 37% copper

Accepted Solution

A:
Answer:36.14 pounds of 34% copper alloy and 9.86 pounds of 48% copper alloyStep-by-step explanation:         First alloy contains 34% copper and the second alloy contains 48% alloy. We wish to make 46 pounds of a third alloy containing 37% copper.        Let the weight of first alloy used be $$x$$ in pounds and the weight of second alloy used be $$y$$ in pounds.        Total weight = $$46\text{ }pounds=x+y$$        $$-(i)$$       Total weight of copper = $$37\%\text{ of 46 pounds = }34\%\text{ of }x\text{ pounds + }48\%\text{ of }y\text{ pounds }$$        $$\dfrac{37\times 46}{100}=\dfrac{34x}{100}+\dfrac{48y}{100}\\\\ 34x+48y=1702$$        $$-(ii)$$        Subtracting 34 times first equation from second equation, $$34x+48y-34x-34y=1702-34\times46\\14y=138\\y=9.857\text{ }pounds \\x=36.143\text{ }pounds$$∴ 36.14 pounds of first alloy and 9.86 pounds of second alloy were used.