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Problem 183

Algebra Difficulty 1.3 Multiple choice CEMC Gauss (Grade 7) · Canada · 2014

If $9210-9124=210-\Box$ , the value represented by the $\Box$ is

Pick one

Official solution

Solution 1

Evaluating the left side of the equation, we get $9210-9124=86$ .

Therefore the right side of the equation, $210-\Box$ , must also equal 86.
Since $210-124=86$ , then the value represented by the $\Box$ is 124.

Solution 2

Since $9210-9124=(9000+210)-(9000+124)=9000-9000+210-124=210-124$ , then the value represented by the $\Box$ is 124.

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