M7MBA wrote:A rectangular tiled patio is composed of 70 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 70 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
A. 5
B. 6
C. 10
D. 13
E. 28
Let R = the number of rows and C = the number of columns.
Total number of tiles = RC.
Since there are 70 tiles, we get:
70 = RC.
We can PLUG IN THE ANSWERS, which represent the value of R.
The equation in blue indicates that the value of R must be a FACTOR OF 70.
Of the five answer choices, only A and C divide evenly into 70.
Eliminate B, D and E.
After the layout changes so that there are 4 more rows and 2 fewer columns, the number of tiles remains 70.
Thus:
70 = (R+4)(C-2).
The equation in red indicates that R+4 must be factor of 70.
Option A implies that R+4 = 5+4 = 9, which is NOT a factor of 70.
Eliminate A.
The correct answer is
C.
C: 10 rows
Current arrangement:
70 = 10C
C = 7.
After the layout changes, there are 4 more rows (for a total of 14 rows) and 2 fewer columns (for a total of 5 columns);
70 = 14*5.
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