Maths Olympiad Prep

Library / /94 of 213

, 2013

Algebra Difficulty 1.4 Junior Find the answer Canada

If x=4x=4 and 3x+2y=303x+2y=30, what is the value of yy?

Pick one

Solutions — 2

Solution 1

Substituting x=4x=4 into 3x+2y3x+2y we get, 3(4)+2y=12+2y3(4)+2y=12+2y.

Since this expression 12+2y12+2y is equal to 30, then 2y2y must equal 301230-12 or 18.
If 2y=182y=18, then yy is 18÷218\div2 or 9.

Solution 2

Each face of a cube is a square. The dimensions of each face of the cube are 1 cm by 1 cm. Thus, the area of each face of the cube is 1×1=11\times1=1 cm2^2.
Since a cube has 6 identical faces, the surface area of the cube is 6×1=66\times1=6 cm2^2.

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.