[bonanova]

Did you read this, Professor? Y-san was looking at the lead

story in today's Daily Blurb:

"Vandals broke into the Flight of Fancy Bird Boutique last night,

and more than half of their pet birds were stolen. Of the birds

still in the store, 1/3 are parakeets, 1/4 are cockatiels, 1/7 are

canaries, 1/8 are lovebirds and 1/9 are parrots."

No, I didn't see that. Is that the whole story?

No, there's more: "The Boutique had exactly 300 birds before

the break-in, and the original number of canaries was double

the number of parakeets still in their cages."

The Professor took a puff on his pipe. Something doesn't seem right.

Well, the reporter says he's not sure about the numbers. He thinks

that one of his fractions might be wrong.

Well, does it say how many canaries were stolen?

No, Professor, but you hang around BrainDen a lot, why don't you

ask someone there?

[Guest]

Parakeets-50

Cocakatiels-37

Canaries-20

Love Birds-18

Parots-16

[Izzy]

but 200 canaries were stolen? So.. I set up fractions.

Still in cages: 2016/6048, 1512/6048, 864/6048, 756/6048, 612/6048

Multiply parakeets by 2. Then cross multiply.

4032/6048 = x/300

x = 200.

I didn't do anything with wrong fractions, so *shrugs*.

[Yoruichi-san]

Err...I must be missing something b/c I have 2 possible answers...

The 1/7 must be the incorrect fraction. Since the number of birds must be a whole number (or I should hope so...;P), the number of remaining birds must be divisible by all the numbers in the denominators except the wrong one.

The least common multiple of 3,4,7,8,9 is the LCM of 7,8,9, which is 504. The LCM of 3,7,8 is 168, and the LCM of 4,7,9 is 252, which are all too large, since the number of remaining birds has to be less than 150 (half of 300).

So that makes the LCM 72 and the fractions 1/3,1/4,13/72,1/8,1/9. So the remaining number of birds could either be 72 or 144. If it's 72, then the current number of parakeets is 24, meaning the original number of canaries is 24*2=48, so 48-13=35 canaries were stolen. If it's 144, then the original number number of canaries was 96, and the number stolen is 96-26=70.

[bonanova]

Err...I must be missing something b/c I have 2 possible answers...

The 1/7 must be the incorrect fraction. Since the number of birds must be a whole number (or I should hope so...;P), the number of remaining birds must be divisible by all the numbers in the denominators except the wrong one.

The least common multiple of 3,4,7,8,9 is the LCM of 7,8,9, which is 504. The LCM of 3,7,8 is 168, and the LCM of 4,7,9 is 252, which are all too large, since the number of remaining birds has to be less than 150 (half of 300).

So that makes the LCM 72 and the fractions 1/3,1/4,13/72,1/8,1/9. So the remaining number of birds could either be 72 or 144. If it's 72, then the current number of parakeets is 24, meaning the original number of canaries is 24*2=48, so 48-13=35 canaries were stolen. If it's 144, then the original number number of canaries was 96, and the number stolen is 96-26=70.

You got it ... my bad for not ruling out 144.