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Algebra Difficulty 1.4 Junior Find the answer Canada

In the diagram, the number placed in each rectangle must equal
the sum of the numbers in the two rectangles directly below it. For
example, the rectangles containing $1$ and $3$ are directly below the rectangle containing $x$ , and so $x=1+3=4$ . What is the value of $y$ ?

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Solution

We begin by labelling the rectangles as shown below.

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In the diagram, $p=9+2=11$ . Since $p+q=18$ , then $q=18-11=7$ . Also, $2+r=q=7$ and so $r=7-2=5$ . Since $s=r+1=5+1=6$ and $x=1+3=4$ , then $y=s+x= 6+4=10$ .

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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.