Olympiad Maths Prep

Track / Stage 4 / 208 of 340 #468 of 2000

Problem 468

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

[ Arithmetic. Mental calculation, etc. ] [ Problems on percentages and ratios ]

Two woodcutters, Ivan and Prokhor, were working together in the forest and sat down to have a snack. Ivan had 4 loaves, and Prokhor had 8. Suddenly, a hunter approached them.

- Well, brothers, I got lost in the forest, the village is far away, and I am very hungry. Please, share your bread and salt with me!
- Well, sit down, we'll share what we have, - said the woodcutters.

The twelve loaves were divided equally among the three of them. After the meal, the hunter rummaged through his pockets, found a hryvnia and a half-ruble, and said:

- Don't be offended, brothers, I don't have anything else. Share the money as you see fit!
- The hunter left, and the woodcutters started arguing.

Prokhor says:

- I think the money should be divided equally!

But Ivan objects:

- For 12 loaves - 60 kopecks, so each loaf is 5 kopecks. Since you had 8 loaves - you get 40 kopecks, I had 4 loaves - I get 20 kopecks!

And how would you divide the money between the woodcutters?

#

Official solution

Note that each eater gets 4 flatbreads.

## Solution

Each eater got 4 flatbreads, which means Ivan ate all his flatbreads himself, while Prokhor gave half of his flatbreads to the hunter. This means that Prokhor should receive all 60 kopecks.

## Answer

Prokhor should receive all the money.

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