The Mystery Number...

We let $x$ be the number. Then we have

$0.35(x)=105$ $\color{#3D99F6}\large \implies$ $x=\dfrac{105}{0.35}=$ $\color{#D61F06}\large \boxed{300}$ $\large \boxed{answer}$

here it is:

$35\%$ % is = $105$

or, $1\%$ % is= $\frac{105}{35}$

or, $100\%$ % is= $\frac{105 \times 100}{35}$ = $300$

The problem statement can be written as

$35\%$ of $N=105$

" $of$ " means multiplication, so

$\dfrac{35}{100}(N)=105$

$N=300$

N * 35/100 = 105
So n = 105 * 100/35 = 300