by defining and solving the linear equation, we conclude that the tray number 55 is the one that will have 102 more gray tiles than white tiles
Which of Tillie’s trays will have 102 more gray tiles than white tiles?
First, let's count the number of each color of tile in each of the given tray.
Tray 1:
10 white tiles.
2 gray tiles.
Tray 2:
14 white tiles.
6 gray tiles.
Tray 3:
18 gray tiles.
12 gray tiles.
Now we need to find patterns here.
First, we can see that the number of white tiles increases by a fixed amount of 4 in each consecutive tray.
The number of gray tiles increases first by 4, then by 6, then by 8, and so on.
Then if n is the number of the tray, the number of white tiles is:
W(n) = 10 + (n - 1)*4
The number of gray tiles is:
G(n) = 2 + (4)*(n - 1) + n*2
Now, we will have 102 more gray tiles than white tiles when:
G(n) = 102 + W(n)
So we can solve that linear equation:
2 + (4)*(n - 1) + n*2 = 10 + (n - 1)*4 + 102
2 + 4n - 4 + 2n = 10 + 4n - 4 + 102
2 + 2n = 10 + 102 = 112
2n = 112 - 2 = 110
n = 110/2 = 55
So, by defining and solving the linear equation, we conclude that the tray number 55 is the one that will have 102 more gray tiles than white tiles.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
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