Question

A metal worker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 120 kg of a 45% copper alloy?

Answer 1

The metalworker should combine 48 kg of 30% copper alloy and 72 kg of 55% copper alloy to make 120 kg of 45 5 copper alloy

Solution:

Let "x" be the amount of 30% copper alloy used in the mix

Then 120 - x will be the amount of 55% copper alloy used in mix

The total amount of copper in the mix is then,

$30 \% \times x + 55 \% \times (120 - x) = 45 \% \times 120\\\\0.30x + 0.55(120 - x) = 0.45 \times 120\\\\0.30x + 66 - 0.55x = 54\\\\-0.25x = 54 -66\\\\-0.25x = -12\\\\x = 48$

Thus 48 kg of 30% copper alloy used in the mix

Then (120 - x) = 120 - 48 = 72

Thus 72 kg of 55% copper alloy used in mix

Thus the metalworker should combine 48 kg of 30% copper alloy and 72 kg of 55% copper alloy to make 120 kg of 45 5 copper alloy