There were a total of 50 blue, red and white marbles in a box. The number of blue and red marbles was $\frac{2}{5}$ of the total number of marbles. The number of red and white marbles was $\frac{9}{10}$ of the total number of marbles. Find the number of red marbles.

1. Find the number of blue and red marbles

$\frac{2}{5} \times 50 = 20$

2. Find the number of red and white marbles

$\frac{9}{10} \times 50 = 45$

3. Find the number of red marbles by adding the two groups and subtracting the total

$\text{Blue} + 2 \times \text{Red} + \text{White} = 20 + 45 = 65$
$\text{Red} = 65 - 50 = 15$