Maths Olympiad Prep

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, 2025

Algebra Difficulty 1.2 Junior Find the answer Canada

A theatre has 600600 seats.
Exactly 25%25\% of these seats are
filled. All of the people in the seats then move to an empty theatre
that has 200200 seats. What percentage
of the seats in the smaller theatre are now filled?

Pick one

Solution

Since 25%25\% of 600600 is 25100×600=25×6=150\dfrac{25}{100}\times600=25\times6=150,
then 150150 people move to the empty
theatre.

The percentage of the seats now filled in the smaller theatre is $150200×100%=1502%=75%$.\$\dfrac{150}{200}\times 100\%=\dfrac{150}{2}\%=75\%\$.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.