Math CentralQuandaries & Queries


Question from Shelly, a parent:

My son brought home a problem of 3 chickens of different weights listing their weights in different groupings of 2. We are to determine the weight of all three together. I think it's a ratio problem, but I am too far removed to formulate a plan to teach him how to solve it.

Hi Shelly,

I like this problem a lot partly because there are so many ways to solve it. If your son knows some algebra he can solve it using the algebraic technique used on the web site.

This problem can however be presented to a student as soon as he or she learns to do arithmetic with decimals. I think this is wonderful problem to give to a group of such students and have them work on a joint solution. I am going to use the numeric values in the problem referred to above and refer to the three chickens as a rooster, a hen and a chick with the rooster the heaviest and the chick the lightest.

The rooster and the chick weigh 8.5 kg and the hen and chick weigh 6.1 kg. Thus the rooster weighs 8.5 - 6.1 = 2.4 kg more than the chicken. But the rooster and the hen together weigh 10.6 kg. Hence, on the scale with the rooster and the hen replace the rooster by an identical hen and a 2.4 kg weight. The scale will still read 10.6 kg. Remove the 2.4 kg weight and the scale reads 10.6 - 2.4 = 8.2 kg. Thus two chickens weigh 8.2 kg. What does one chicken weigh?

A third solution comes from an observation. What does 10.6 + 8.5 + 6.1 = 25.2 kg represent in terms of roosters, hens and chicks?

I hope this helps,


I think I might know what you mean, and if so, it's not a ratio problem but a problem in linear algebra.

Are the data in a form like:

X and Y together weigh A
Y and Z together weigh B
Z and X together weigh C ?

This gives rise to the linear equation system

x + y       = A
      y + z = B
x       + z = C

This isn't in triangular form, so has no obvious "weak spot." But you can (for instance) subtract the second equation from the first to get a second equation in x and z; then add this to the third to eliminate z.

Good Hunting!

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