Solution To: A Weighty Problem

Here it is folks, the solution you all have been waiting for (or at least that's what I like to tell myself). 

Here is the original problem.

Here are the answers.  All three chickens combined weigh 12.4 kg.   The small chicken weighs 1.8 kg., the medium chicken weighs 4.3 kg., and the large kg. weighs 6.3 kg.

Now here is how you figure all of that out.

Looking at the problem, if you add the weights given to you in the first three illustrations, then you are adding the weights of two large chickens, two medium chickens, and two small chickens.  You want to find the combined weight of one large chicken, one medium chicken, and one small chicken.  So, add the weights given to you in the first three illustrations, and divide it by two. 

So you would have 10.6 + 8.1 + 6.1 = 24.8.   Then divided this by two.  24.8/2 = 12.4.  Therefore, all three of the chickens together weigh 12.4 kg (don't forget your units at the end of your answer...that's a no-no!).

Finding the weight of each individual chickens is a bit more complicated and you are going to have to recall some algebra skills.  I am going to label the large chicken L, the medium chicken M, and the small chicken S. 

This is what we know from the question we just answered.

L + M + S = 12.4

From illustration number 3, we know that     M + S = 6.1 .    So, we are going to substitute 6.1 in for  M + S  in the equation up above.  So we now have   L + 6.1 = 12.4 .  Now we just subtract 6.1 from both sides to get L by itself.  This yields 6.3 .   So the large chicken weighs 6.3 kilograms.

Using illustration number one, we know that    M + L = 10.6 .  We also know (because we just figured it out) that L = 6.3 .  So again, we are going to substitute 6.3 in for L.  That gives us,  M + 6.3 = 10.6 .   Then you subtract 6.3 from both sides to get M by itself.  That gives us 4.3 .   So the medium chicken weighs 4.3 kg.

Lastly, using illustration number two, we know that    S + L = 8.1 . We also know that L = 6.3 . So again, we are going to substitute. That gives us,  S + 6.3 = 8.1 . Then you subtract 6.3 from both sides to get S by itself. That gives us 1.8 . So the small chicken weighs 1.8 kg.

And Voila!  For the second question, you pretty much had to use substitution to find the weights of the individual chickens but you could have found their weight in any order that you wanted to.

Maybe this one was tougher than I thought it would be.  But hopefully you'll come back next Friday for a new problem of the week, unless you're too chicken.

Sincerely,
The Math Freak