Maths Olympiad Prep

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, 2023

Algebra Difficulty 1.1 Junior Find the answer Canada

If 3+x=53+x=5 and 3+y=5-3+y=5, then x+yx+y equals

Pick one

Solution

Since 3+x=53+x = 5, then x=2x = 2.

Since 3+y=5-3+y = 5, then y=8y = 8.

Thus, x+y=10x+y=10.

Alternatively, we could have added the original two equations to obtain
(3+x)+(3+y)=5+5(3+x)+(-3+y) = 5+5 which simplifies
to x+y=10x+y=10.

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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.