A square countertop has a square tile inlay in the cente, leaving an untiled stripof uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width in inches of the strip?

a) 1.5

b) 3

c) 4.5

A) a only

B) b only

C) a and b only

D) a and c only

E) a, b and c

I believe this is the full question.

Now say X is the length of one of the sides of the Square counter-top. And there is another small square tile in between the larger square. The smaller square leaves equal width on all four sides.

Now given that the ratio of Tiled portion to Untiled portion is 25/39

So tiled portion is a multiple of 25 and untiled portion is a multiple of 39.

We can rewrite the ratio as 25y/39y where y is the common multiple of 25 and 39.

y can be any positive integer.

the area of the tile will be = 25y and area of untiled portion = 39y

Now the area of the counter-top = X² = Area of tile + Area of untiled portion = 25y + 39y = 64y

when y=1, X²=64 and X=8 and Area of tiled portion = 25, length of side of tile = 5

width of untiled portion = (8-5)/2 =1.5

When y=2, width = 3

When y=3, width = 4.5

So answer is E. All three are possible widths of the untiled portion.

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