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, 2019

Algebra Difficulty 1.6 Junior Find the answer Canada

Each of $w,x,y$ , and $z$ is an integer. If $w+x=45$ , $x+y=51$ , and $y+z=28$ , what is the value of $w+z$ ?

Pick one

Solution

The first scale shows that [[IMAGE0]] has the same mass as [[IMAGE1]] .

The second scale shows that [[IMAGE2]] has the same mass as [[IMAGE3]] .

Therefore, the sum of the masses of [[IMAGE4]] and [[IMAGE5]] is equal to the sum of the masses of [[IMAGE6]] and [[IMAGE7]] .

That is, the equal-arm scale shown below is balanced.

[[IMAGE8]]

The left and right sides of this scale each contain a [[IMAGE9]] , and the scale remains balanced if one [[IMAGE10]] is removed from each side of the scale (since they are equal in mass).

That is, the equal-arm scale shown below is balanced.

[[IMAGE11]]

Therefore of the answers given, [[IMAGE12]] has the same mass as [[IMAGE13]] .

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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.