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Bunuel
A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28

The various rectangles that can be formed are 70*1, 35*2, 10*7, and 14*5.

If we remove 2 tiles from each row, the rectangles 70*1 and 35*2 will not remain rectangular

Lets consider 10 rows of 7 tiles each. If we remove 2 tiles each, we will be left with 14 rows of
5 tiles each which will be shaped like a rectangle.

Therefore, there were 10 rows(Option C) in the tile floor before the change in layout happened.
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Hi Guys,

Can someone explain me what happens to the nx term in the 2nd and the 3rd line of the solution below..

Thanks in advance,

JCA
nick1816
Let number of rows = n, and number of tiles in each row= x

Given that- nx=70 and (n+4)(x-2)=70

(n+4)(x-2)=70
nx+4x-2n-8=70
70+4x-2n-8=70
2x-n=4
\(\frac{140}{n} - n = 4\)
n=10 and x=7



Bunuel
A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28
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avellanjc
Hi Guys,

Can someone explain me what happens to the nx term in the 2nd and the 3rd line of the solution below..

Thanks in advance,

JCA
nick1816
Let number of rows = n, and number of tiles in each row= x

Given that- nx=70 and (n+4)(x-2)=70

(n+4)(x-2)=70
nx+4x-2n-8=70
70+4x-2n-8=70
2x-n=4
\(\frac{140}{n} - n = 4\)
n=10 and x=7



Bunuel
A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28
We defined that nx = 70, so we substitute the value of nx in the third line which moves to RHS and gets subtracted to give 0. We are left with 4x - 2n - 8 = 0 => 4x - 2n = 8 => 2x - n = 4
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Krunaal,

My bad. Wasnt able to see that substitution.

Thanks very much!
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