Question

a metal worker has a metal alloy that is 20% copper, and another metal alloy that is 60% copper. How many kilograms (kg) of each allow should the metal worker combine to create 80kg of aa 52% copper alloy?

Answer 1

Let X = the 29% alloy and Y = the 60% alloy.

They want a total of 80kg, so you have X +Y = 80

Rewrite that to get X = 80-Y

You also want 0.20X + 0.60Y = 0.52(80)

Replace X with 80-y:

0.20(80-y) + 0.60y = 0.52(80)

Simplify:

16 - 0.20y + 0.60y = 41.6

Combine like terms:

16 +0.40y = 41.6

Subtract 16 from each side:

0.40y = 25.6

Divide both sides by 0.40

y = 25.6 / 0.40

y = 64

Now you have Y replace y with 80 in X = 80-Y

X = 80 - 64

X = 16

They need 64 Kg of the 60% alloy and 16 Kg of the 20% alloy.