EXPLANATION
Let's see the facts:
3 friends ----> $360
ratio: 2:3:4.
In order to obtain the ratio, we need to calculate the unit ratio as shown as follows
[tex]\text{First friend = }\frac{2}{(2+3+4)}\cdot360=\frac{2}{9}\cdot360=80[/tex][tex]\text{Second friend = }\frac{3}{(2+3+4)}\cdot360=\frac{3}{9}\cdot360=120[/tex][tex]\text{Third friend = }\frac{4}{(2+3+4)}\cdot360=\frac{4}{9}\cdot360=160[/tex]Answer: the third friend received the largest share-----> $160.