Question

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

Answer 1

Answer:

36.14 pounds of 34% copper alloy and 9.86 pounds of 48% copper alloy

Step-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.