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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