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## Chicken Little

Posted by Chris on March 28, 2012 – 4:12 pm

This one’s especially for Knightmare.

If a chicken weighs 10 lbs plus half its weight, how much does the chicken weigh?

The last time this was posted, it got a staggering 112 replies (mostly with the wrong answer). I’ll post a link to it later.

This post is under “MathsChallenge” and has 23 respond so far.

### 23 Responds so far- Add one»

1. 1. Kel9902 Said：

20 lbs

2. 2. Thrym Said：

unless i’m mssing something the equation should be
w = 10 + .5w
then
2w = 20 + w
w = 20
seems pretty straight forward

3. 3. Chris Said：

Are you sure?

4. 4. Kel9902 Said：

yes

5. 5. SP Said：

Its weight is 20 lbs.

10 lbs + half of its weight
= 10 lbs + (1/2 * 20 lbs)
= 10 lbs + 10 lbs
= 20 lbs

6. 6. Daniel Said：

15 lbs.

7. 7. Chris Said：

YEEESSSSSS! We have at least one wrong answer

8. 8. DP Said：

That’s a prety heavy chicken. But 20 lbs it is. I think this one was set up too well…we knew it was tricky going in to it =)
Thanks for keeping ‘em coming Chris.

9. 9. Chris Said：

It’s 17.5 lbs

10. 10. Chris Said：

Only joking.

If w is the weight of the chicken, then the chicken weighs,
w = 10 + w/2 => w = 20

For info there is a pound mass and it weighs 1 lb. There is also the slug, it’s about 32 lbs mass.

11. 11. DP Said：

I love Rajesh’s answer about half way down that post. Barely any math needed…

logic: entire weight = half of weight + half of weight

problem: entire weight = 10 + half of weight

the term directly to the right of the “=” say half of weight and 10 are the same. So if 10 is half of the weight, then per the first (logic) equation; entire weight = 10 + 10 = 20.

12. 12. DP Said：

If you prefer the math approach, you can subtract my previous equations or set them equal. I’ll do both.

subtraction:
entire weight = half of weight + half of weight
mius
entire weight = 10 + half of weight
gives
0 = (half of weight – 10) + 0
0 = half of weight – 10
10 = half of weight
multiply by 2
20 = entire weight

equivalent:
entire weight = half of weight + half of weight
entire weight = 10 + half of weight
set “entire weight” equal to “entire weight”
gives
half of weight + half of weight = 10 + half of weight
subtact “half of weight” from both sides
half of weight = 10
multiply both sides by 2
entire weight = 20

13. 13. Chris Said：

I’ll check that out on wolframalpha.com. I just hope their server is up to the task.

14. 14. Chris Said：

Hi DP. Thanks for posting Rajesh’s solution. It’s very nice.

15. 15. Chris Said：

w = 10 + w/2
If the weight of the chicken is an integer, then:
w = w/2 (mod 5) => 2w = w (mod 5) => w = 0 (mod 5)
So w = 5, 10, 15, 20, 25, 30, 35…

In mod 7 we get
w = 3 + w/2 (mod 7) => 2w = 6 + w (mod 7) => w = 6 (mod 7)
=> w = 6, 13, 20, 27, …
So the smallest possible candidate positive integer weight is 20.
The next candidate will be at 20 + lcm(5,7) = 20 + 35 = 55
Subsequent candidate weights will be in steps of 35 => 90, 125…

Unfortunately I can only peck away (ho ho) the values.
Another modulo base might eliminate 20.

16. 16. Chris Said：

I forget to mention that the chicken had a sister in hatch 1 and at least one brother.

17. 17. Chris Said：

w = 10 + ½(10 + ½(10 + ½(10 + …
= 10 + 10(½ + ¼ + ⅛ + …)
= 10 + 10*1
= 20

18. 18. fida Said：

10 + 10/2 = 15 lbs

19. 19. Chris Said：

Hi Daniel and fida. The answer really is 20 lbs.

See post 11 for a really easy way to see why it’s 20 lbs.

Your mistake is due to the way you are reading the question. You have said (to yourself) that the chicken weighs 10 lbs, and then in effect changed your mind and added the extra 5 lbs.

You can see that 20 is right by doing the same thinking but by knowing in advance that 20 is the weight. Then you get 10 + 20/2 = 20.

Also once you’d decided 15 was the answer, you should have checked to see if your answer worked. You could perhaps then try, 15 + 15/2 = 17.5 and then using that new value tried 17.5 + 17.5/2 = 22.5 and so on. You’d find the weight just gets bigger and bigger – so that’s not the right way to check. You could also have tried 10 + 15/2 = 17.5 and then 10 + 17.5/2 = 18.75 and then 10 + 18.75/2 = 19.375 and as you continue you’d get closer and closer to 20, but you’d never quite get there. That should be a hint that your first answer can’t be right either.

Because it doesn’t matter in what order you add up (e.g. 3+4 = 4+3), you could read the question as, “if a chicken weighs half it’s weight plus 10 lbs, how much does the chicken weigh?” Then using 20, it’s clearer that you’d get 20/2 + 10.

Back to algebra. We have w = w/2 + 10 => 2w = w + 20 => w = 20

I suspect that both of you are very young and aren’t really quite happy with arithmetic or algebra. Ask your maths teacher to explain it to you.

20. 20. Eketahuna Said：

as per Thrym # 2 : Straightforward quadratic equation

x = 10 + .5x
multiply both sides by 2

2x = 2(10 + .5x)
2x = 2*10 + 2*.5x
2x = 20 + x

subtract x from both sides

2x – x = 20 + x – x
x = 20

21. 21. Linda Said：

10 lbs. The chicken weighs 10 lbs as stated.

22. 22. Chris Said：

Hi Linda. Why not skip more and read it as “If a chicken weighs 1 lb …” or “if a chicken weighs half its weight…”?

23. 23. atma Said：

15 lbs

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