Olympiad Maths Prep

Track / Stage 4 / 191 of 340 #451 of 2000

Problem 451

AMC 12 late, AIME early
Number theory Difficulty 4.8 Find the answer

79. - Tell me, famous Pythagoras, how many students attend your school and listen to your discourses?

- In all, 一 replied the philosopher: - half study mathematics, a quarter study music, a seventh part remains in silence, and, in addition, there are three women.

Official solution

79. We form the equation:

12x+14x+17x+3=x \frac{1}{2} x+\frac{1}{4} x+\frac{1}{7} x+3=x

from which x=28x=28. We can solve the following problems arithmetically as well.

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