How many kilograms (kg) of a 15% copper alloy must be melted with a 45% copper alloy to obtain 60 kilograms of 32% copper alloy?

Let 'x' represent the amount of 15% copper alloy

let 'y' represent the amount of 45% copper alloy.

Form 2 equations.

Eq. 1: x+y = 60

Meaning: x amount of 15% alloy + y amount of 45% alloy = 60 kg.

Eq. 2: 0.15x+0.45y=0.32 (60)

Meaning: 15% of alloy x + 45% of alloy y = 60kg of 32% alloy.

Use substitution or elimination to solve this linear system. I used substitution, meaning that I would need to rearrange equation 1.

x=y=60

y=60-x

Substitute equation 1 into equation 2.

0.15x+0.45 (60-x) = 0.32 (60)

0.15x+27-0.45x=19.2

-0.3x=-7.3

x=26

Substitute x=26 into equation 1 or 2. In this case, equation 1 is simpler.

x+y=60

26+y+60

y=34

To check, substitute the values of x and y into equation 2.

0.15x+0.45y=0.32 (60)

0.15 (26) + 0.45 (34) + 19.2

3.9+15.3+19.2

19.2=19.2

∴26kg of 15% copper alloy and 34kg of 45% copper alloy would be needed to obtain 60kg of 32% copper alloy.

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