Olympiad Maths Prep

Track / Stage 4 / 312 of 340 #572 of 2000

Problem 572

AMC 12 late, AIME early
Combinatorics Difficulty 5.0 Find the answer

4. Charity. A generous person distributed the same amount of money equally among those who asked him for assistance every week. One day he noticed:

- If the number of petitioners is five less next week, each will receive two dollars more.

But, alas, after a week, the number of petitioners did not decrease but increased by four.

- This means,--the benefactor noted,--that each will receive one dollar less.

How much did each petitioner receive this last time?

Official solution

4. At first, there were 20 people and each received 6 dollars. Fifteen people (five fewer) would have received 8 dollars each. But their number increased to 24 (by four people), and each received only 5 dollars. Thus, the weekly donation amount is 120 dollars.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.