SOLUTION: 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 to

Algebra.Com
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.
~~~~~~~~~~~~~~~~~~~ 

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.

-------------------------------------------------------------

Answers:
Total weight = 12.4 kg
Individual weights = 4.3 kg and 6.3 kg and 1.8 kg
RELATED QUESTIONS

Three chickens were weighed in pairs. The first pair weighed in at 10.6 kilograms, the... (answered by Earlsdon)
Three chickens were weighed in pairs; the first pair weighed in at 10.6 kg, the second... (answered by Fombitz)
Three chickens were weighed in pairs; the first pair weighed in at 10.6 kg, the second... (answered by scott8148)
Three chickens were weighed in pairs; the fist pair weighed in at 10.6 kg, the second... (answered by ankor@dixie-net.com)
When the melons were weighed in pairs each pair weighed more than 100 pounds. smith's... (answered by checkley71)
Ann, Beth and Celine wanted to weigh themselves, but the scales they had were broken and (answered by stanbon)
Could you help me, please? I need to answer this: 1-When a baby was born, she weighed (answered by josgarithmetic)
hannah test grades were 80,85,72 and 92. What is her weighted average if the test grades... (answered by ankor@dixie-net.com)
A certain scale only registers weights that are greater than 6 pounds. A person who... (answered by stanbon)