Question

An alloy of Copper and Aluminum has 45% Copper. An alloy of Copper and Zinc has Copper and
Zinc in the ratio 3:6. These two alloys are mixed in such a way that in the overall alloy, there is more
Aluminum than Zinc, and Copper constitutes a fraction x of this alloy. What is the minimum value of
x (as a fraction)?

Answer 1

Answer:

29/73

Step-by-step explanation:

An alloy of Copper and Aluminum has 45% Copper. An alloy of Copper and Zinc has Copper and

Zinc in the ratio 3:6. These two alloys are mixed in such a way that in the overall alloy, there is more

Aluminum than Zinc, and Copper constitutes a fraction x of this alloy. What is the minimum value of

x (as a fraction)?

Let say Alloy of Copper and Aluminum taken =  100A

Then Copper = 45A   & Alumium = 55A

& Let Say Copper & Zinc = 9B

Copper = 3B   & Zinc = 6B

Then total  100A + 9B

Copper = 45A + 3B  

Aluminium = 55A

Zinc = 6B

55A > 6B

Let say 55A = 6B + k

=> 6B = 55A - k

x =  (45A + 3B)/(100A + 9B)

x = (45A + 55A/2 - k/2)/(100A + 3*55A/2 - 3k/2)

x = (145A/2 - k/2)/(365A/2 - 3k/2)

x = (145A - k)/(365A - 3k)

Lim k -> 0

x = 145A/365A  = 29/73