Olympiad Maths Prep

Track / Stage 4 / 207 of 340 #467 of 2000

Problem 467

AMC 12 late, AIME early
Number theory Difficulty 4.9 Find the answer

1. Long ago, nine identical books cost 11 rubles and some kopecks, while thirteen such books cost 15 rubles and some kopecks. How much did one book cost?

From the first condition, it follows that one book costs more than 122 kopecks, otherwise 1229=1098122 \cdot 9=1098 kopecks. Thus, the price of one book is 123 kopecks.

Official solution

Answer: 123 kopecks.

Criteria: correct answer without explanation - 2 points.

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