Question

A metalworker has a metal alloy that is 25​% copper and another alloy that is 55​% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 43​% copper​ alloy?

Answer 1

The metalworker should combine 40 kg of the 25% copper alloy with 60 kg of the 55% copper alloy to obtain 100 kg of a 43% copper alloy.

Step-by-step explanation:

Solving Mixture Problems using Algebra

To solve this problem, we can use a system of equations to find out how many kilograms of each alloy the metalworker needs to combine to create 100 kg of a 43% copper alloy. Let x represent the kilograms of the 25% copper alloy and y represent the kilograms of the 55% copper alloy.

• 
  
• The sum of the two alloys should be 100 kg: x + y = 100
• 
  
• The total amount of copper from both alloys should make up 43% of the 100 kg: 0.25x + 0.55y = 0.43 * 100

Solving these two equations simultaneously:

1. 
   
3. From equation (1), y = 100 - x.
4. 
   
6. Substitute y in equation (2) with 100 - x.
7. 
   
9. 0.25x + 0.55(100 - x) = 43
10. 
    
12. Expand the equation: 0.25x + 55 - 0.55x = 43
13. 
    
15. Combine like terms: -0.30x = -12
16. 
    
18. Divide both sides by -0.30: x = 40

Substitute x back into equation (1):

1. 
   
3. y = 100 - 40
4. 
   
6. y = 60

Therefore, the metalworker should combine 40 kg of the 25% copper alloy with 60 kg of the 55% copper alloy to create 100 kg of a 43% copper alloy.

Answer 2

To determine the answer, we need to set up equations. We do this by doing mass balances. We let

x = A alloy 25% copper
y = B alloy 55% copper

Overall Mass balance:

x + y = 100

Copper mass balance:

.25x + .55y = .43(100) = 43

SOlving simultaneously, we get:

x = 99.67 kg 25% copper alloy
y = 0.33 kg 55% copper alloy