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: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.Step-by-step 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, [tex]\frac{\frac{30x}{100} + \frac{55y}{100}  }{x + y} = \frac{50}{100}[/tex] ⇒ 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)