It's party time my friends!

Let $c$ be the number of children, $m$ be the number of men and $w$ be the number of women. So the equations are

$w=2c$ $\color{#D61F06}(1)$

$c=2m$ $\color{#D61F06}(2)$

$c+w+m=35$ $\color{#D61F06}(3)$

From $\color{#D61F06}(2)$ , we get $m=\dfrac{c}{2}$ . Then ,

$c+w+m=35$

$c+2c+\dfrac{c}{2}=35$

$\color{#3D99F6}\boxed{c=10}$

The ratio of $\text{Men : Children : Women} :: 1x:2x:4x$ . Their sum is $35 \implies 7x = 35 \implies x = 5$

$\text{Children } = 2x = \boxed{10}$