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Problem 333

Algebra Difficulty 2.3 Multiple choice CEMC Fermat · Canada · 2022

If $10x + y = 75$ and $10y + x = 57$ for some positive integers
$x$ and $y$ , the value of $x + y$ is

Pick one

Official solution

Since $10x + y = 75$ and $10y + x = 57$ , then $(10x + y) + (10y + x) = 75 + 57$ and so
$11x + 11y = 132$ Dividing by 11, we
get $x + y = 12$ .

(We could have noticed initially that $(x,y)=(7,5)$ is a pair that satisfies the
two equations, thence concluding that $x+y=12$ .)

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