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CEMC Gauss (Grade 7), 2016

Algebra Difficulty 1.6 Junior Find the answer Canada

Each of $\square, \triangle$ and $\blacklozenge$ represents a non-zero number. If $\square=\triangle+\triangle+\triangle$ and $\square=\blacklozenge+\blacklozenge$ , then $\square+\blacklozenge+\triangle$ equals

$\square+\triangle$
$\blacklozenge+\triangle+\triangle+\triangle+\triangle$
$\blacklozenge+\blacklozenge+\square$
$\triangle+\triangle+\triangle+\blacklozenge+\blacklozenge$
$\blacklozenge+\blacklozenge+\blacklozenge+\triangle+\triangle$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $\square=\triangle+\triangle+\triangle$ , then by adding a $\blacklozenge$ to each side we get $\square+\blacklozenge=\blacklozenge+\triangle+\triangle+\triangle$ .

Since $\square+\blacklozenge=\blacklozenge+\triangle+\triangle+\triangle$ , then by adding a $\triangle$ to each side we get that $\square+\blacklozenge+\triangle=\blacklozenge+\triangle+\triangle+\triangle+\triangle$ .

(Can you explain why each of the other answers is not equal to $\square+\blacklozenge+\triangle$ ?)

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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.