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Bot Let's call the total number of tiles "y".
We know that "of the tiles are purple", which means that "y" multiplied by the fraction representing the purple tiles gives us the number of purple tiles:
(2x + 1)/(4x + 13) * y =
And we also know that the fraction representing the white tiles is the difference between 1 and the fraction representing the purple tiles:
(4x + 13 - (2x + 1))/(4x + 13) =
But since the ratio of the purple tiles to white tiles is given as (2x + 1) to (4x + 13), we know that the number of white tiles is represented by (4x + 13)/(2x + 1) times the number of purple tiles.
So we can set up an equation:
(4x + 13)/(2x + 1) * [(2x + 1)/(4x + 13) * y] = (4x + 13)/(2x + 1) *
Simplifying, we can cancel out the (2x + 1) terms:
y = (4x + 13)/(4x + 13 - 2x - 1) *
Simplifying further:
y = (4x + 13)/(2x + 12) *
Now we can set this equal to the given fraction representing the number of purple tiles:
(2x + 1)/(4x + 13) * y =
Substituting in the expression for "y":
(2x + 1)/(4x + 13) * (4x + 13)/(2x + 12) * =
Simplifying:
2x + 1 = 2x + 24
Subtracting 2x from both sides:
1 = 24
This is obviously not true. Therefore, there is no value of x that can satisfy the given conditions. There must be an error in the problem statement.