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Algebra Difficulty 1.7 Junior Find the answer Canada

$X$ is 20% of 50. 40 is 20% of $Y$ . 40 is $Z$ % of 50. What does $X+Y+Z$ equal?

Pick one

Solution

We begin by recognizing that there are 6 different symbols, and so each face of the cube contains a different symbol.

From left to right, let us number the views of the cube 1, 2 and 3.

Views 1 and 2 each show a face containing the symbol [[IMAGE0]] .

What symbol is on the face opposite to the face containing [[IMAGE1]] ?

In view 1, [[IMAGE2]] and [[IMAGE3]] are on faces adjacent to the face containing [[IMAGE4]] , and so neither of these can be the symbol that is on the face opposite [[IMAGE5]] .

In view 2, [[IMAGE6]] and [[IMAGE7]] are on faces adjacent to the face containing [[IMAGE8]] , and so neither of these can be the symbol that is on the face opposite [[IMAGE9]] .

There is only one symbol remaining, and so [[IMAGE10]] must be the symbol that is on the face opposite [[IMAGE11]] , and vice versa.
A net of the cube is shown below.

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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.