Rebecca S.

asked • 10/11/20

Square Tiles Problem~ Algebra 1

In a house, all rooms are square and covered with white congruent tiles. Tiles along the diagonal are PURPLE and other tiles are WHITE.


There are 77 PURPLE tiles on the BATHROOM floor.

There are 1,296 TOTAL tiles on the LAUNDRY ROOM floor.


Which room uses more white tiles? How many more white tiles does this room use?

2 Answers By Expert Tutors

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David W. answered • 10/11/20

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Angel S.

Yes, but this doesn’t account for the tile in the middle of the floors that is purple. The equation I used is x+(x-1) and my answer is that there are 219 more white tiles. Does this answer make sense?
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10/11/20

David W.

Yes, this does account for the tile(s) in the center of the room. As an array, you could refer the the purple tiles as B(1,1), B(2,2), ... B(77,77). That makes 77 purple tiles. The laundry room could be table with 36 purple tiles labeled L(1,1), L(2,2), ... L(36,36). Subtract the purple tiles from the total to get the number of white tiles. Which room uses more white tiles? How many more white tiles does this room use?"
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10/11/20

David W.

NOTE: To clarify "middle," draw a 3x3 and a 4x4 grid. When there is an odd number of tiles in each row&column, there is a tile there. When there is an even number of tiles in each row&column, there is a corner there.
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10/11/20

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