Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146.

Let one part be $\mathrm{x}$.

7 times the first part $=7 \mathrm{x}$

Let the other part be $(24-\mathrm{x})$.

5 times the second part $=5(24-\mathrm{x})$

$\therefore 7 x+5(24-x)=146$

$\Rightarrow 7 x+120-5 x=146$

$\Rightarrow 7 x-5 x=146-120$

$\Rightarrow 2 x=26$

$\Rightarrow x=\frac{26}{2}=13$

Therefore, one part is 13 .

Other part $=(24-x)=(24-13)=11$