Lorraine is placing tiles in rows.In each succeeding row,she doubles the number of tiles.The ninth row has 768 tiles.How many tiles did Lorraine use in the first row?
Well, let me do some quick calculations here. *Puts on oversized clown glasses and takes out miniature calculator* If Lorraine doubles the number of tiles in each row, we can work our way backwards. So, if the ninth row has 768 tiles, the eighth row must have half that, which is 384 tiles. And if each row before that has half the number of tiles, we can keep going until we reach the first row. Hold on, let me do some preposterous counting... *Flips calculator upside down, squints at it* Ah yes, the first row must have... *dramatic pause* ...2 tiles! So Lorraine started off with just 2 tiles and managed to build up to 768. Quite the tile magician, I must say.
To find out how many tiles Lorraine used in the first row, we need to work backwards, starting from the ninth row.
Let's assume that in the ninth row, Lorraine used x number of tiles. According to the given information, the ninth row has 768 tiles.
Now, we'll work backwards from the ninth row to the first row, doubling the number of tiles in each row:
Ninth row: x
Eighth row: 2x
Seventh row: 4x
Sixth row: 8x
Fifth row: 16x
Fourth row: 32x
Third row: 64x
Second row: 128x
First row: 256x
Given that the ninth row has 768 tiles, we can set up the following equation to find x:
256x = 768
Now, we can solve for x by dividing both sides of the equation by 256:
x = 768 / 256
x = 3
Therefore, Lorraine used 3 tiles in the first row.
To find out how many tiles Lorraine used in the first row, we need to work backwards from the ninth row.
In the ninth row, Lorraine had 768 tiles. In the previous row, she would have had half as many tiles as in the ninth row. So, we divide 768 by 2 to find the number of tiles in the eighth row.
768 ÷ 2 = 384
In the same way, we divide the number of tiles in the eighth row by 2 to find the number of tiles in the seventh row.
384 ÷ 2 = 192
We continue this process until we reach the first row.
Dividing 192 by 2 gives us the number of tiles in the sixth row:
192 ÷ 2 = 96
Dividing 96 by 2 gives us the number of tiles in the fifth row:
96 ÷ 2 = 48
We repeat again to find the number of tiles in the fourth row:
48 ÷ 2 = 24
Continuing, we find:
24 ÷ 2 = 12 (number of tiles in the third row)
12 ÷ 2 = 6 (number of tiles in the second row)
6 ÷ 2 = 3 (number of tiles in the first row)
Therefore, Lorraine used 3 tiles in the first row.