Ridiculously easy Maths question

[Vivitrix]

Why hello!

There's been a bit of heated discussion in my office between my boss, his daughter and I concerning the apprentices (boss' son) key skills assignment (gcse grade stuff).

Basically it asks you to measure a room, length by width, and calculate how many tiles of a known size that can fit in said room.

The width by length is 2100x2880mm. So area therein is 6048000mm.

The tiles are 300mm^2 (squared). This is where the confusion and arguing and over analysing comes from. The question is worded badly.

Boss is saying the area is 300mm and therefore the length x width is 17.32mm by 17.32mm due to sqrt of the 300. (this seems a bit too small and inherently wrong to me)

Whereas I see it saying the tiles are 300x300, therefore 90000 in area.

With the way i see I get a total of 67.2 tiles needed. (6048000\(300^2)

Whereas the bosses is 20160. (6048000\300).

So the calculations are right but the how the area is being viewed isn't. Any ideas?

[Skraa]

I think you should take it literal, and assume 300mm^2 size is correct in the math problem. It's small for a tile, but when you're doing mosaic for example totally plausible.

Also you did crucial part of the math wrong if you're taking it really literally. You should not calculate area but dimensions when calculating the number of tiles you can fit in, ie. (2100mm/17.32mm) * (2880mm/17.32mm) = 20086 tiles.

[Ensar]

Yeah, these are always terribly worded so that you can never be sure you're right. We used to have to sit there and try and workout how some text books got their answers back in high school as they often interpreted their own questions in the most bizarre of ways. Often we spent longer playing strange version of countdown over doing what the questions intended.


Anyway, even when you do as Skraa say's you're still not sure what they want. As we're dealing with tiles here, which we're assume to be square. Using lengths to workout areas won't work as we'll need to deal with partial tiles too.

When we get 121.247... and 166.281... tiles down each side, it doesn't work with whole tiles. You'll need 121*166 full tiles and then 121+166+1 partial tiles. Which brings the question, how you make these partial tiles? By cutting them down? In that case how much 'edge' do we want on them? Could we cut one tile into 3 parts, or do we need to have manufactured edges on each of them? Can't work out how many they wand there without give you more information. So do we count each part as a whole tile? If we do we'll need 121*166+121+166+1 = 122*167 = 20374.

So many places where you can fail here, and yet still be using a perfectly fine logical line of working.

[Skraa]

Anyway, even when you do as Skraa say's you're still not sure what they want.

When we get 121.247... and 166.281... tiles down each side, it doesn't work with whole tiles. You'll need 121*166 full tiles and then 121+166+1 partial tiles.

Yep. My approach was very literal interpretation of "how many tiles can you fit" question, with no partials allowed. It's bit too vague question, but maybe that's the point and the rating is based on how you analyze it and follow through with math.

When it comes to the 300x300mm question, it's possible if the exact wording is "300mm square", but if it says 300mm^2 then there's no real room for interpretation.

[Posix]

No-one is taking grout into account!

[Vivitrix]

Linoleum tiles, your argument is invalid.

[Posix]

What about consideration of the tiles expanding and contracting as heat conditions change?

[Vivitrix]

Ah, Touche'.

[Mansen]

Or the bonding solution that goes between each tile

[Rowain]

As for the original question (area or square tile side length): since you cannot calculate the number of tiles needed without knowing the actual side lengths (see below), it must be side length. Area is not enough as you can get the same area with and infinite combinations of side lengths, most giving slightly different results.

If we assume that 300 is side length (which also makes much more RL sense), solution is simple: [width / sideLength] * [length / sideLength] where square brackets denote rounding up. Working with areas directly (total area / tile area) is incorrect as you cannot buy partial tiles.

So it is [2100 / 300] * [2880 / 300] = [7] * [9.6] = 7 * 10 = 70

[Skraa]

As for the original question (area or square tile side length): since you cannot calculate the number of tiles needed without knowing the actual side lengths (see below), it must be side length. Area is not enough as you can get the same area with and infinite combinations of side lengths, most giving slightly different results.

At least here in Finland things like floor tiles are sold in m^2 although with known dimensions.

[Selassie]

In sweden, they always ask for exact dimension of your room. Because they do not trust people to calculate themselves what they need. And.... then they fail themselves and give you the wrong amount.

But we're quiet pretty people on the other hand!

[Rowain]

Yep, the price is usually determined by the total area of the tiles bought, but that still means an actual (integer) number of tiles.

[Posix]

You should add 10% for breakages too!

[Idreil]

Hmm, well wall are never 100% square, roofs and ceilings are never 100%, when your tiling you usually work with estimates.

As you buy tiles per Square meter you work out the square meter of the room you need to add, and as posix said, add 10% to breakages. Most of the time if you work it out like this you will have a possble few full tiles left that you can stick in the attic when the tiles are no longer made and one breaks you can still replace the tile.
If you are 1 box short... easy, buy one more box.


Now if you do not really want to buy tiles and you just care about the math it can get alot more technical as you should prolly have the 300x300 changed to 303x303 for the grouting. also the thickness of the tile will matter when you get to a corner where 2 tiles meet plus the tile glue. It can get very complicated if you want it to be.