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

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.