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Algebra Difficulty 1.7 Junior Find the answer Canada

In a group of seven friends, the mean (average) age of three of the friends is 12 years and 3 months and the mean age of the remaining four friends is 13 years and 5 months. In months, the mean age of all seven friends is

Pick one

Solution

In the diagram, rectangles $WQRZ$ and $PXYS$ are the two sheets of 11 cm $\times$ 8 cm paper.

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The overlapping square $PQRS$ has sides of length 8 cm.

That is, $WQ=ZR=PX=SY=11$ cm and

$WZ=QR=PS=XY=PQ=SR=8$ cm.

In rectangle $WQRZ$ , $WQ=WP+PQ=11$ cm and so

$WP=11-PQ=11-8=3$ cm.

In rectangle $WXYZ$ , $WX=WP+PX=3+11=14$ cm.

Since $WX=14$ cm and $XY=8$ cm, the area of $WXYZ$ is

$14\times8=112$ cm $^2$ .

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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.