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MATH WORD PROBLEMS

J&T TILING COMPANY ONLY TILE SQUARE AREAS AND USE ONLY SQUARE TILES. THEY ALSO ONLY USE ONE PATTERN. ANN PLACES   THE CENTER  WITH WHITE TILES. BEN COMES ALONG AND BOARDERS THE AREA WITH GRAY TILES. HOW MANY BOARDER TILES ARE NEEDED FOR A 20x20 AREA/?  FOR A KxK AREA?
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1 Answer

Well, one would think the full 20 would be needed for the first opposing sides (whether top and bottom, or left and right) and 18 would complete the interior of the other sides of the border, so (20 x 2) + (18 x 2) or 40 + 36 which = 76.  Our generic formula would then be (K x 2) + ((K-2) x 2) = border tiles.  If you need to simplify that, it could be 2K + 2k-4, or
4k-4 so for our original 20 x 20, it would be 4(20)-4 or 80 - 4 which is again, 76.

Comments

Some dis-ambiguity may be required:
This is assuming the 20 x 20 INCLUDES the border tiles upon completion.
If we're measuring by Ann placing a 20  x 20 center of white tiles, and THEN the border is added,
the formula becomes,
((K + 2) x 2 ) + (K+2-2) x 2  which simplifies to 2K + 4 + 2K, or 4K PLUS 4
Thanks so much for your explanation to this word problem. Yes I just needed to know where to plug in the right numbers!