Using proportions, supposing that 30% of the tiles are purple, it is found that the value of x is of x = 16.
A proportion is a fraction of a total amount.
In this problem, the ratio of purple tiles to white tiles is given by:
[tex]\frac{2x + 1}{4x + 13}[/tex]
We consider that 30% of the tiles are purple, hence 70% are white, which means that:
[tex]\frac{2x + 1}{4x + 13} = \frac{3}{7}[/tex]
Applying cross multiplication:
14x + 7 = 12x + 39
2x = 32
x = 16.
The value of x is of x = 16.
More can be learned about proportions at https://brainly.com/question/24372153
