Question

A metalworker has a metal alloy that is 20​% copper and another alloy that is 65​% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 56​% copper​ alloy?

The metalworker should use _kilograms of the metal alloy that is 20​% copper and _kilograms of the metal alloy that is 65​% copper.
​(Type whole​ numbers.)

Answer 1

The metallurgist must use 20 kilograms of the metal alloy which is 20% copper and 80 kilograms of the metal alloy which is 65% copper.

Explanation:

We call the alloy 20% copper.

We call the alloy 65% ​​copper.

Let's call the new version you want to create.

When mixing the M Alloy with the S you want to obtain 100 kg of the new alloy

`M + S = 100` (i)

Then

`0.2M + 0.65S = 100(0.56)` (ii)

We substitute (i) in (ii)

`0.2(100-S) + 0.65S = 100(0.56)`

`20 - 0.2S + 0.65S = 56`

`0.45S = 36`

`S = (36)/(0.45)`

`S = 80 kg` (iii)

Now we substitute (iii) in (i)

`M + 80 = 100`

`M = 20`