In a lake, there is a patch of llily pads. every day, the patch doubles in size. if it takes 243 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

If the patch doubles in size every day, it means that yesterday it was half as large as today. So, if today (day 243) the patch is as large as the lake, yesterday (day 242) half as large, so it was as large as half the lake.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: