Question

A metalworker has a metal alloy that is 20​% copper and another alloy that is 70​% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 50​% copper​ alloy?

Answer 1

40 kilograms alloy of 20 % copper and 60 kilograms of alloy of 70 % copper is combined to get 100 kg of 50 % copper alloy

Solution:

Th final alloy is 100 kg

Let "x" be the alloy of 20 % copper

Then, (100 - x) is the alloy of 70 % copper

Therefore,we can say,

"x" kilograms alloy of 20 % copper and (100 - x) kilograms of alloy of 70 % copper is combined to get 100 kg of 50 % copper alloy

Therefore, we frame a equation as:

`x * 20 \% + (100-x) * 70 \% = 100 * 50 \%\\\\x * (20)/(100) + (100-x) * (70)/(100) = 100 * (50)/(100)\\\\0.2x + (100-x) * 0.7 = 0.5 * 100\\\\0.2x + 70 - 0.7x = 50\\\\-0.5x = -20\\\\x = 40`

Thus 40 kilograms of 20 % copper

Then, 100 - x = 100 - 40 = 60

60 kilograms of 70 % copper is used