Answers:
20 kg of the 20% copper alloy
80 kg of the 75% copper alloy
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Work Shown:
x = amount (in kg) of the 20% copper alloy
y = amount (in kg) of the 75% copper alloy
We want the final alloy to be 100 kg, so x+y = 100. Solving for y gets us y = 100-x. We will use this later.
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We have x kilograms of the 20% alloy so we have 0.20x kilograms of pure copper from this batch alone.
Then we have y kilograms of the 75% alloy, adding on 0.75y kilograms of more pure copper.
In total, we have 0.20x+0.75y kilograms of pure copper.
We want 64 kilograms of pure copper since 64% of 100 = 0.64*100 = 64
Therefore 0.20x+0.75y = 64 is the second equation to set up.
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Use substitution to solve for x.
0.20x+0.75y = 64
0.20x+0.75( y ) = 64
0.20x+0.75( 100-x ) = 64 .... plug in y = 100-x
0.20x+0.75(100)+0.75(-x) = 64 ... distribute
0.20x+75 - 0.75x = 64
-0.55x+75 = 64
-0.55x = 64-75 .... subtract 75 from both sides
-0.55x = -11
x = -11/(-0.55) .... divide both sides by -0.55
x = 20
Use this x value to find the value of y
y = 100-x
y = 100-20
y = 80
So the solution is (x,y) = (20,80)
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Let's check those two values
x+y = 20+80 = 100, so that works out
A = 0.20x = 0.20*20 = 4 kg of pure copper from the 20% batch
B = 0.75y = 0.75*80 = 60 kg of pure copper from the 75% batch
A+B = 4+60 = 64 kg of pure copper from both batches
Answers are confirmed.
