Math help!?

Question

Help with this problem, and i need the steps.

A flock of geese on a pond were being continuously observed. At 1 PM, 1 fifth flew away. At 2 PM, 1 eighth flew away. At 3 PM, 3 times as many geese as had flown away at 1 flew away, leaving 28 geese on the pond. No other geese arrived or flew away than stated above. How many geese were in the original flock?

srry, it is 1 eighth of the remaining, and 3x 1PM of the rremaining

Answer 1

Let F be the number of geese in the original flock.

There are two ways to approach this. In the first, we assume that when you say one-eight flew away that you mean one-eight of the ORIGINAL flock. In that case, the math is

F - F/5 - F/8 - 3F/5 = 28

Multiply through by 40

40F - 8F - 5F - 24F = 1120
3F = 1120
F = 373 1/3 which is not an integer.

So now let's assume that when you say one-eighth flew away, that's one-eight of the REMAINING flock. Then the math is

F - F/5 - (4F/5)(1/8) -3F/5 = 28

Multiply through by 40 again...

40F - 8F - 4F - 24F = 1120
4F = 1120
F = 280

The second interpretation yields an integer solution of 280 geese in the original flock.