Question

A metallurgist has one alloy containing 32% copper and another containing 65% copper. How many pounds of each alloy must he use to make 44 pounds of a third alloy containing 42% copper? (Round off the answers to the nearest hundredth.)

Answer 1

Answer:

30.67 pounds of 32% copper alloy and 10.33 pounds of 65% copper alloy

Step-by-step explanation:

        First alloy contains 32% copper and the second alloy contains 65% alloy.

We wish to make 44 pounds of a third alloy containing 42% 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 = $44\text{ }pounds=x+y$        $-(i)$

      Total weight of copper = $42\%\text{ of 44 pounds = }32\%\text{ of }x\text{ pounds + }65\%\text{ of }y\text{ pounds }$

       $\dfrac{42\times 44}{100}=\dfrac{32x}{100}+\dfrac{65y}{100}\\\\ 32x+65y=1848$        $-(ii)$

       Subtracting 32 times first equation from second equation,

$32x+65y-32x-32y=1848-32\times44\\33y=440\\y=13.333\text{ }pounds \\x=30.667\text{ }pounds$

∴ 30.67 pounds of first alloy and 13.33 pounds of second alloy were used.