SOLUTION: Three chickens were weighed in pairs. The first pair weighed in at 10.6 kilograms, the second pair weighted 8.5 kg, and the third pair weighed 6.1 kg. How much would the scale

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Question 11175: Three chickens were weighed in pairs. The first pair weighed in at 10.6 kilograms, the second pair weighted 8.5 kg, and the third pair weighed 6.1 kg.
How much would the scale read if all three chickens were weighed at the same time?
How much does each chicken weigh?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the weight of the 1st chicken = x, the weight of the 2nd = y, and the weight of the 3rd = z.
1) x+%2B+y+=+10.6
2) y+%2B+z+=+8.5
3) x+%2B+z+=+6.1
Now we need to solve for x, y, and z. We have a system of three equations with three unknowns.
Let's rewrite two of the three equation and substitute into the third one.
1) x+%2B+y+=+10.6 rewrite as: x+=+10.6+-+y
2) y+%2B+z+=+8.5 rewrite as: z+=+8.5+-+y Substitute these into the 3rd equation and solve for y.
3) x+%2B+z+=+6.1 or
%2810.6+-+y%29+%2B+%288.5+-+y%29+=+6.1 Simplify and solve for y.
19.1+-+2y+=+6.1 Add 2y to both sides.
19.1+=+2y+%2B+6.1 Subtract 6.1 from both sides.
13+=+2y Divide both sides by 2.
y+=+6.5
From the rewritten equation 1):
x+=+10.6+-+y
x+=+10.6+-+6.5
x+=+4.1
From the rewritten equation 2):
z+=+8.5+-+y
z+=+8.5+-+6.5
z+=+2
The chickens weigh 4.1 kgs, 6.5 kgs, and 2 kgs.
The three chickens would together, weigh x + y + z or 4.1 + 6.5 + 2 = 12.6 kgs.