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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.)

User Zollie
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1 Answer

3 votes

Answer:

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

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 }


(42* 44)/(100)=(32x)/(100)+(65y)/(100)\\\\ 32x+65y=1848
-(ii)

Subtracting 32 times first equation from second equation,


32x+65y-32x-32y=1848-32*44\\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.

User MarvinVK
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