A farmer is trying to cross a river. He is taking with him a rabbit, carrots, and a fox, and he has a small raft. He can only bring 1 item at a time across the river because his raft can only fit either the rabbit, the carrots, or the fox. How does he cross the river? (Assume that the fox does not eat the rabbit if the man is present, and that the fox and the rabbit will not try to escape or run away).

Answers from prior postings

Question #1 -
Let D = number of dollars on the check, and C = number of cents on the check, where D and C are whole numbers.

The amount of the check has a value of 𝐷+𝐶100 dollars. The teller swaps the dollars and cents and gives the woman 𝐶+𝐷100 dollars.

The woman spends 5 cents (5100 𝑑𝑜𝑙𝑙𝑎𝑟𝑠), so she is left with 𝐶+𝐷− 5100 dollars.

That amount of money she has is equal to two times the amount of the check.

Therefore, 𝐶+𝐷− 5100 = 2(𝐷+𝐶100).

100𝐶+𝐷−5 = 200𝐷+2𝐶.

199D = 98C – 5

Intuition is needed to derive the second equation.

We know that the number of cents of the check must be less than 100.

Since the amount that the women received was 5 cents more than twice the amount of the check once the dollars and cents were switched, the number of dollars must be less than 50.

In addition to that, the number of cents must be 1 more than twice the dollar amount.

Therefore, C = 2D + 1

199D = 98(2D +1) – 5

199D = 196D +93

3D = 93

D = 31

C = 2(31) + 1 = 63

The amount of the check was $31.63

Question #2   -
Null Island is the name used to refer to the point on the Earth's surface where the Prime Meridian and the Equator intersect, at zero degrees latitude and zero degrees longitude (0°N 0°E). This point is located in international waters in the Gulf of Guinea, in the Atlantic Ocean, off the coast of West Africa. The point is marked with a permanent buoy.