CSMC 2023 Part A - Question 4, CEMC UWaterloo

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Difficulty: 6

This problem is tagged with csmc, csmc23, highschool.

(Canadian Senior Mathematics Contest 2023, Part A, Question 4, CEMC - UWaterloo)

A store sells shirts, water bottles, and chocolate bars. Shirts cost $ \$ 10$ each, water bottles cost $ \$ 5$ each, and chocolate bars cost $ \$ 1$ each. On one particular day, the store sold $x$ shirts, $y$ water bottles, and $z$ chocolate bars. The total revenue from these sales was $ \$ 120$. If $x$, $y$ and $z$ are integers with $x \gt 0$, $y \gt 0$ and $z \gt 0$, how many possibilities are there for the ordered triple $(x, y, z)$?

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