A metal worker has a metal alloy that is 20% copper and another alloy that is 75% copper. How many kilograms of each alloy should the metal worker combine to create 90 kg of a 64% copper alloy?

he needs to combine 18 kg

of the 20% copper alloy and 72 kg of the 75% copper alloy.

Step-by-step explanation:

Let x represent the number of kilograms of the 20% copper alloy that he needs to use.

Let y represent the number of kilograms of the 75% copper alloy that he needs to use.

The mass of the copper to be created is 90 kg. It means that

x + y = 90

The amount copper in the first alloy is 20/100 × x = 0.2x

The amount copper in the second alloy is 75/100 × y = 0.75y

The amount of copper in the alloy to be created is

64/100 × 90 = 57.6

The equation would be

0.2x + 0.75y = 57.6- - - - - -- - - - - 1

Substituting x = 90 - y into equation 1, it becomes

0.2(90 - y) + 0.75y = 57.6

18 - 0.2y + 0.75y = 57.6

- 0.2y + 0.75y = 57.6 - 18

0.55y = 39.6

y = 39.6/0.55

y = 72

x = 90 - y = 90 - 72

x = 18

-4

step-by-step explanation: