I was on a job interview and I was required a couple of tests - some of it was general information, some math and some logic. I did OK except for this one - I spent about 20 minutes on it before I gave up and wrote down a guess. Can anyone give me a hand on this?
A fish’s head is 9" long. The tail is the length of the head plus 1/2 the body. The body is the length of the head and the tail. What is the total length of the fish?
Nausicaa
Is the length of the body the length of the fish, or is the fish head + body + tail?
[spoiler]
head is 9 inches
body is 36 inches
tail is 27 inches
therefore, either the fish is 36 inches, or it is 9 + 36 + 27 = 72 inches[/spoiler]
Algebra would look like this. T = tail, B = body.
9 + 1/2B = T
9 + T = B
Then you can just solve for 2 variables.
Turn it into a math problem
Total length of fish = H + T + B
H for head 9
T for tail length 9 + 1/2B
B for body length 9 + T
Solve for Body length, first substitute in the equation for tail then just do the algebra
B = 9 + T
B = 9 + (9 + 1/2B)
B = 18 + 1/2B
1/2b = 18
B = 36
Now that you have B, plug it into the equation for T
T = 9 + 1/2B
T = 9 + 1/2(36)
T = 9 + 18
T = 27
So know we know all 3 variables, substitute into H + B + T
9 + 36 + 27
The fish is 72 inches long
ETA: The above answers were posted while I was typing mine, which essentially just repeats what they say.
t = 9 + (1/2)b
b = 9 + t
Substituting 9 + (1/2)b for t in the second equation yields b = 9 + 9 + (1/2)b
Solving for b gives b = 36.
Then t = 27
Total = 9 + 36 + 27
Thanks! I was close but I just couldn’t quite get it.
The implication is that body does not include head nor tail, the way I read it? Very badly worded. One would assume a fish body includes the head. The whole is stupid because how do you tell where a fish head ends? (End of the gils?) How many fish other than maybe a Manta have a tail over half the length of the body? (For a Manta, I’d call it the stinger maybe, not a tail?)
“Fred’s feet are the length of his head plus half the length of his body…”
325F for 20 min, season with a little lemon juice and dill. Eat the fish.
Problem solved. 
72"
I got the same as everyone else, 72.
That said, I think this:
Should also have concluded “That’s one hell of a big fish… Recipe feeds 24, use a bigger oven.”
[quote=“md2000, post:7, topic:550657”]
The implication is that body does not include head nor tail, the way I read it? Very badly worded. One would assume a fish body includes the head. The whole is stupid because how do you tell where a fish head ends? (End of the gils?) How many fish other than maybe a Manta have a tail over half the length of the body? (For a Manta, I’d call it the stinger maybe, not a tail?)
QUOTE]
Seconded . Very badly worded problem .
Body does not include head & tail ? :eek:
I got the same answer as everyone else.
I want to know where you went that gave you this question, 'cause I would so kick ass at that interview.
No, that’s simply wrong. It will take much more than 20 minutes. 
Apparently the all-tackle angling record Striped bass, taken in New Jersey in 1972, weighed 78 ½ pounds and measured 72 inches long
I interpreted “The body is the length of the head and the tail” to mean that the entire fish is the head plus the tail; IOW the fish’s body is divided up into the head and the tail. Then I got 36" as the answer.
This is one of those lateral thinking puzzles. The correct answer is, “Give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime.”
The fish is 72 inches long.
3 parts to the fish: the Head (H), the Body (B) and the tail (T). I set B = X, there are other ways to do it as well but this works fine.
This information was given in the problem:
H = 9"
B = H+T = X
T = H+0.5B = 9+0.5X
Now solve for B (i.e., solve for X)
X = H+T
X = 9+9+0.5X
X = 18+0.5X
X - 0.5X = 18
X = (18/0.5)
X = 36 = B
So…
H = 9
B = 36
T = H+0.5B = 9+(0.5*36) = 27
9+36+27 = 72 inches.
doh! didn’t see godix’s excellent post above.
People, people, please. The question says “The body IS the length of the head and the tail.” It doesn’t say “The body is equal to…”
The fish has a body. Some of it is head, some of it is tail, but everything is either one or the other.
H = 9
T = 9 + (H +T)/2
2(T-9)= H + T
T = H + 18
T = 27
H = 9
So B = 36", not 72", because fish=body. Fish != head+body+tail.
Hm… that is an interesting interpretation of the question that I hadn’t considered. Very poorly worded in my opinion.
Have you ever eaten a fish? :dubious:
BTW we don’t know if the language given by the OP is exactly the wording on the test.