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Problem 182

Combinatorics Difficulty 1.2 Multiple choice CEMC Fermat · Canada · 2026

Leah went for a walk and recorded the number of robins, cardinals
and blue jays that she saw in the bar graph shown. Unfortunately, she
forgot to include numbers on the vertical axis. If a total of $30$ robins, cardinals and blue jays were
observed, how many robins did she see?

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Official solution

The bar graph shows that $6$ times as many robins were observed as blue jays, and $3$ times as many cardinals were observed as blue jays. Suppose that $x$ blue jays were observed. Then $6x$ robins were observed and $3x$ cardinals were observed. A total of $30$ birds were observed, and so $x+6x+3x=30$ or $10x=30$ , and so $x=3$ . On her walk, Leah observed $6x=6(3)=18$ robins.

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