## Euclid 2022 Question 3, CEMC UWaterloo

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#### Difficulty: 5

#### This problem is tagged with euclid, euclid22, highschool.

**(Euclid 2022, Question 3, CEMC - UWaterloo)**

(a) A large water jug is $\frac{1}{4}$ full of water. After $24$ litres of water are added, the jug is $\frac{5}{8}$ full. What is the volume of the jug, in litres?

(b) Stephanie starts with a large number of soccer balls. She gives $\frac{2}{5}$ of them to Alphonso and $\frac{6}{11}$ of them to Christine. The number of balls that she is left with is a multiple of $9$. What is the smallest number of soccer balls with which Stephanie could have started?

(c) Each student in a math club is in either the Junior section or the Senior section. No student is in both sections.

Of the Junior students, $60\%$ are left-handed and $40\%$ are right-handed.

Of the Senior students, $10\%$ are left-handed and $90\%$ are right-handed.

No student in the math club is both left-handed and right-handed.

The total number of left-handed students is equal to the total number of righthanded students in the math club.

Determine the percentage of math club members that are in the Junior section.

*Answer Submission Note(s)*

Drop the percent sign in part (c) and separate your answers with a single space.

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