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CEMC Gauss (Grade 8), 2013

Algebra Difficulty 1.6 Junior Find the answer Canada

Sally is asked to multiply $\frac{2}{3}$ and $1\frac{1}{2}$ . Jane is asked to add them. The difference between Sally’s answer and Jane’s answer is

Pick one

Solution

The total area of the shaded regions is the difference between the area of square $JKLM$ and the area of the portion of rectangle $PQRS$ that overlaps $JKLM$ .

Since $JK=8$ , then the area of square $JKLM$ is $8\times8$ or 64.

Since $JK$ is parallel to $PQ$ , then the portion of $PQRS$ that overlaps $JKLM$ is a rectangle, and has length equal to $JK$ or 8, and width equal to $PS$ or 2.

So the area of the portion of $PQRS$ that overlaps $JKLM$ is $8\times2=16$ .
Therefore the total area of the shaded regions is $64-16=48$ .

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