A metalworker has a metal alloy that is 20 % copper and another alloy that is 60 % copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 52 % copper alloy?

16 kg of I type and 64 kg of II type should be mixed.

Step-by-step explanation:

Given that a metal alloy in original has 20% copper and 80% other metals.

Another mixture contains 60% copper and 40% other metals.

We have to get a new alloy of 80 kg which has 52% copper.

Let us assume that we mix x kg of I alloy and y kg of second alloy.

Then we have x+y = total weight = 80 kg.

x+y = 80 ... (i)

Next condition is that new alloy has 52% copper in it

When we mix x kg of I, and y kg of II, copper content would be

0.2x+0.6y. This equals 52% of 80 = 41.6

Or Dividing by 0.2 we get

x+3y = 208 ... (ii)

(ii) - (i) gives 2y = 128 or y = 64 kg

x = 16 kg

16 kg of I type and 64 kg of II type should be mixed.

Verify:

Copper in new alloy = 16 (0.2) + 64 (0.6) = 3.2+38.4 = 41.6

= 52% of 80