Question

A metalworker 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 80 kg of a 45​% copper​ alloy?

Answer 1

• 32 kg of 30% copper
• 48 kg of 55% copper

Explanation:

Let x represent the mass of 55% copper alloy that is to be used in the mix. Then 80-x is the mass of 30% copper alloy to be used. The total amount of copper in the mix is then ...

... 0.55x + 0.30(80-x) = 0.45·80

... 0.25x = 12 . . . . . . simplify, subtract 24

... x = 48 . . . . . . . . . divide by the coefficient of x

... 80-x = 32 . . . . . . the mass of 30% copper alloy required

The metalworker should combine 32 kg of 30% copper alloy with 48 kg of 55% copper alloy to make 80 kg of 45% copper alloy.