Problem is in description

Question

A metal worker has a metal alloy that is 15% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metal worker combine to create 60 kilogram's of a 42% copper alloy?

Answer 1

Let x = kg of 15% copper alloy

Let y = kg of 60% copper alloy

 

Since we need to create 60 kg of alloy we know:

x + y = 60

 

42% of 60 kg = 25.2 kg of copper

 

So we're interested in creating 25.2 kg of copper

We need some amount of 15% copper and some amount of 60% copper to create 25.2 kg of copper:

 

0.15x + 0.60y = 25.2

but

x + y = 60

x= 60 - y

 

substituting that value in for x

 

0.15(60 - y) + 0.60y = 25.2

9 - 0.15y + 0.60y = 25.2

0.45y = 16.2

y = 36

 

Substituting this y value to solve for x gives:

 

x + 36 = 60

x = 24

 

Therefore, in order to create 60 kg of a 42% alloy, we'd need 24 kg of 15% copper and 36 kg of 60% copper.

Answer 2

x = 15%

y = 60%

 

x + y = 60  (this shows the weights)

.15x + .60y = .42(60)   (this shows the percentages)

15x + 60y = 42(60)

15x + 60y = 2520

 

15x + 15y = 900  (multiply weight equation by 15)

          45y = 1620 (subtract from weight equation)

 

y = 36

 

The alloy should contain 36K of 60% and 24K of 15%.