Answer:
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 [tex]x[/tex] in pounds and the weight of second alloy used be [tex]y[/tex] in pounds.
Total weight = [tex]44\text{ }pounds=x+y[/tex] [tex]-(i)[/tex]
Total weight of copper = [tex]42\%\text{ of 44 pounds = }32\%\text{ of }x\text{ pounds + }65\%\text{ of }y\text{ pounds }[/tex]
[tex]\dfrac{42\times 44}{100}=\dfrac{32x}{100}+\dfrac{65y}{100}\\\\ 32x+65y=1848[/tex] [tex]-(ii)[/tex]
Subtracting 32 times first equation from second equation,
[tex]32x+65y-32x-32y=1848-32\times44\\33y=440\\y=13.333\text{ }pounds \\x=30.667\text{ }pounds[/tex]
∴ 30.67 pounds of first alloy and 13.33 pounds of second alloy were used.
