Maths Olympiad Prep

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, 2020

Algebra Difficulty 1.2 Junior Find the answer Canada

In the pie chart shown, 80 students chose juice. How many students chose milk?

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Solution

Solution 1

One complete rotation equals 360°360\degree. Since 90°90\degree is 90°360°=14\frac{90\degree}{360\degree}=\frac14 of one complete rotation, then 14\frac14 of all students chose juice. Therefore, the remaining 114=341-\frac14=\frac34 of all students chose milk. Since 34\frac34 is 3×143\times\frac14, then 3×80=2403\times80=240 students chose milk. Solution 2 As in Solution 1, 14\frac14 of all students chose juice. Since the 80 students who chose juice represent 14\frac14 of the total number of students, then the total number of students is 4×80=3204\times80=320. Therefore, 32080=240320-80=240 students chose milk.

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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.