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Explore the Back-StoryTry this beautiful Set theory Problem based on Set theory from PRMO - 2016.

In a school there are 500 students. Two-thirds of the students who do not wear glasses, do not bring lunch. Three-quarters of the students who do not bring lunch do not wear glasses. Altogether, 60 students whowear glasses bring lunch. How many students do not wear glasses and do not bring lunch?

Set theory

Intersection and Union of Sets

Solving equations of several variables

Challenges and Thrills of Pre-college Mathematics

PRMO 2016 Problem 5

240

Divide the children into four parts :

m: Those who don't wear glasses, and don't bring lunch.

n: Those who wear glasses but don't bring lunch.

p: Those who bring lunch but don't wear glasses.

q : Those who do bring lunch and wear glasses.

Try to find information and form equations

There can be following equations formed:

$m + n + p + q =500.$

$ m = \frac{2}{3}(m + p)$

$m=\frac{3}{4}(m+n)$

$q=60$

Try to solve by finding the values of the different variables

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