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 100 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 30% copper and (blank) kilograms of the metal alloy that is 55% copper. (show your work)

Answer 1

20kg

Explanation:

Answer 2

The metal worker should use 20 kilograms of the metal alloy that is 30% copper and 80 kilograms of the metal alloy that is 55% copper.

Explanation:

Let us assume that x kg of 30% copper alloy and y kg of 55% copper alloy are mixed to form 100 kg of 50% copper alloy.

So, we can write x + y = 100 ......... (1)

⇒30x + 30y = 3000 .......... (2)

Again we can write,
`((30x)/(100) + (55y)/(100)  )/(x + y) = (50)/(100)`

⇒ 30x + 55y = 50 × 100 = 5000 .......... (3)

Now, from equations (2) and (3) we can write

55y - 30y = 2000

⇒ 25y = 2000

⇒ y = 80 Kg.

So, from equation (1), we get,

x = 100 - y = 100 - 80 = 20 Kg. (Answer)