# [MOVED] How many geese were in original flock?

#### lori

##### New member
A flock of geese on a pond were being observed contiuously.
At 1:00 pm 1/5 of the geese flew away.
At 2:00 pm 1/8 of the geese flew away.
At 3:00 pm 3 times as many geese as has flown away at 1:00 pm flew away, leaving 28 geese on the pond. At no other time did any geese arrive or fly away or die. How many geese were in the original flock?

I am at a total loss on this question. If someone could help me get started I would greatly appreciate it!

#### daon

##### Senior Member
Re: HOW MANY GEESE??

lori said:
A flock of geese on a pond were being observed contiuously.
At 1:00 pm 1/5 of the geese flew away.
At 2:00 pm 1/8 of the geese flew away.
At 3:00 pm 3 times as many geese as has flown away at 1:00 pm flew away, leaving 28 geese on the pond. At no other time did any geese arrive or fly away or die. How many geese were in the original flock?

I am at atotal loss on this question. If someone could help me get started I would greatly appreciate it!
Let T be the number of Geese. T will be the total number that flew away plus 28, right?

At 1PM, (1/5)T flew away.

At 2PM, there are only (4/5)T left on the pond, and it is stated that (1/8) of them flew away. So (1/8) of (4/5)T is (1/8)(4/5)T = (1/10)T.

At 3 PM, 3 times the number of geese that flew away at 1PM flew away. This is 3(1/5)T = (3/5)T.

Therefore the total, T, of geese is:

T = (1/5)T + (1/10T) + (3/5)T + 28

Now try to get T by itself.

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: HOW MANY GEESE??

lori said:
A flock of geese on a pond were being observed contiuously.
assume originally started with geese = n

At 1:00 pm 1/5 of the geese flew away. n/5 gone left with (n-n/5 =) 4n/5

At 2:00 pm 1/8 of the geese flew away. Additional (4n/5 * 1/8=)n/10 gone --> (4n/5*7/8=)7n/10 left

Now continue....

At 3:00 pm 3 times as many geese as has flown away at 1:00 pm flew away, leaving 28 geese on the pond. At no other time did any geese arrive or fly away or die. How many geese were in the original flock?

I am at atotal loss on this question. If someone could help me get started I would greatly appreciate it!

#### Denis

##### Senior Member
lori, good idea to "start" by "making up" a case; like take 100 to start:

100 - (1/5 0f 100) = 100 - 20 = 80 : 80 remaining

80 - (1/8 of 80) = 80 - 10 = 70 : 70 remaining

70 - (3 times number that left at first) = 70 - ( 3 times 20) = 70 - 60 = 10 : 10 remaining

So now you know "how it works"; you need to find what original number
will end up with 28, using above steps; HOINK ?!