Question 1205563: Three chickens were weighed in pairs. The first pair weighed in at 10.6 kilograms, the second pair weighted 8.1 kg, and the third pair weighed 6.1 kg. How much do they weigh all together and how much does each chicken weigh.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website! .
Three chickens were weighed in pairs. The first pair weighed in at 10.6 kilograms,
the second pair weighted 8.1 kg, and the third pair weighed 6.1 kg.
How much do they weigh all together and how much does each chicken weigh.
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Let the weights be x, y, and z for the 1st, 2nd and 3rd chick, respectively.
Then we have these equations
x + y = 10.6 (1)
x + z = 8.1 (2)
y + z = 6.1 (3)
To solve, add all three equations. You will get
2x + 2y + 2z = 10.6 + 8.1 + 6.1 = 24.8
hence
x + y + z = 24.8/2 = 12.4. (4)
Thus, all the chicken weight 12.4 kg combined.
To find the weight of the 1st chick, subtract equation (3) from equation (4). You will get
x = 12.4 - 6.1 = 6.3.
To find the weight of the 2nd chick, subtract equation (2) from equation (4). You will get
y = 12.4 - 8.1 = 4.3.
To find the weight of the 3rd chick, subtract equation (1) from equation (4). You will get
z = 12.4 - 10.6 = 1.8.
ANSWER. The weight of the 1st chick is 6.3 kg; 2nd chick 4.3 kg; 3rd chick 1.8 kg.
The combined weight of the three chicken is 12.4 kg.
Solved.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
x,y,z = weight of the 3 chickens
The order doesn't really matter.
Add the weights pairwise
x+y = 10.6
y+z = 8.1
x+z = 6.1
Add straight down as the other tutor mentions to get
2x+2y+2z = 24.8
Divide everything by 2 to get
x+y+z = 12.4
Telling us that all three chickens combine to 12.4 kg
Since x+y+z = 12.4 and x+y = 10.6, we can replace the x+y block with 10.6 to isolate z
x+y+z = 12.4
10.6+z = 12.4
z = 12.4-10.6
z = 1.8 is one of the individual weights.
Once we know z = 1.8, we can plug it into y+z = 8.1 and x+z = 6.1 to find y = 6.3 and x = 4.3 respectively. I'll leave the scratch work for the student to do.
Another way to find x is to use a similar trick that we did to isolate z.
Since x+y+z = 12.4 and y+z = 8.1 we can then say:
x+y+z = 12.4
x+8.1 = 12.4
x = 12.4-8.1
x = 4.3
Once you know 2 of the chicken's individual weights, you can plug them into x+y+z = 12.4 to find the missing variable.
As you can see, there's a few pathways you could take. Feel free to explore your favorite.
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Answers:
Total weight = 12.4 kg
Individual weights = 4.3 kg and 6.3 kg and 1.8 kg
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