Six Geese a Laying

The initial assumption, which should probably be mentioned in the problem, is that each goose produces the same amount of eggs per unit time.

So, you know 6 geese lay 12 eggs in 6 hours. Since each goose produces the same amount per given time frame, that means that 1 goose lays 2 eggs in 6 hours. The question asks how many geese are necessary to produce 100 eggs in a day, which is 4 times the length of the original time period, so the geese are 4x as productive in a day versus 6 hours.

This means 1 goose lays 8 eggs in a day. In order to make at least 100 eggs 8g>= 100 g>=13, since geese can't be fractional

Each lays 1 every 3 hours or 8 per day. So you need at least $\frac{100}{8}= 12.5$ geese, which of course rounds up to 13.

We assume that each Goose lays the same number of Eggs in a given time. Reading the text of the problem, we know that 6 Geese lay 12 Eggs in 6 Hours, so we are sure that 1 Goose lays 2 Eggs in 6 Hours. One day has 4 x 6 Hours, so 1 Goose lays 8 Eggs a Day. Since 12 Geese can lay only 8 x 12=96 Eggs a Day, we need one more Goose to lay at least 4 Eggs in the same Day (to have at least 100 Eggs). 12+1=13 Geese