A box contains a collection of triangular and square tiles. There are 25 tiles in the box and 84 edges. How many square tiles are there in the box?

This problem here would be a little tricky. Let us take into account first the variables presented which are the following: a collection of triangular and square tiles, 25 tiles, and 84 edges. Triangles and squares are 2D in shape so they give us a variable of 3 and 4 to work on those edges. Let us say that we represent square tiles with x and triangular tiles with y. There would be two equations which look like these:

x + y = 25 and 4x + 3y = 84

The first one would refer to the number of tiles and the second one to number of edges.

We will be using the first equation to the second equation and solve for one. So if we will be looking for y for instance, then x in the second equation would be substituted with x = 25 - y which would look like this:

4 (25 - y) + 3y = 84

Solve.

100 - 4y + 3y = 84

-4y + 3y = 84 - 100

-y = - 16

-y/-1 = - 16/-1

y = 16

Then:

x = 25 - y

x = 25 - 16

x = 9

So the answer is that there are 9 square tiles and 16 triangular tiles.