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Problem of the Week
Problem B
Symbolic Shapes

In each question, each shape (\(\Box\), \(\bigcirc\), \(\triangle\)) is equal to the same whole number. For example, \(\Box+\Box=8\) implies that \(2 \times \Box=8\), so \(\Box =4\). (The value of each shape can change from question to question.)

Determine the value of each shape in each question.

  1. \[\begin{aligned} \Box+\Box&=8 \\ \bigcirc+\Box&=10 \end{aligned}\]

  2. \[\begin{aligned} \Box+\Box+\Box&=18 \\ \Box+\bigcirc+\bigcirc&=14\\ \bigcirc+\Box+\triangle&=18 \end{aligned}\]

  3. \[\begin{aligned} \bigcirc+\bigcirc+\bigcirc&=24 \\ \Box\times\bigcirc+\Box&=36\\ \triangle\times\Box+\triangle&=25 \end{aligned}\]

  4. \[\begin{aligned} 2\times\triangle&=28 \\ \triangle-10&=\bigcirc\\ \bigcirc+\Box+\Box&=10 \end{aligned}\]

  5. \[\begin{aligned} \Box+\triangle+\triangle&=21 \\ \triangle+\bigcirc-\Box&=9\\ \Box+\Box&=18 \end{aligned}\]

Extension: Create a similar problem and challenge a classmate to solve it.

Themes: Algebra, Number Sense