The question narrows the groups down from 3 groups with men, women and children to 2 groups with adults and children. Combine the ratios of the men and the women to children to create this new ratio: (3+5):2 = 8:2. You can then simplify it to 4:1.
Let x be the number of children.
[tex]4:1 = (x+360) : x[/tex]
Cross-multiply the two ratios to get the expression below, simplify and solve for x:
[tex]x + 360 = 4x[/tex]
[tex]360 = 4x - x[/tex]
[tex]360 = 3x[/tex]
[tex]x = \frac{360}{3}[/tex]
[tex]x = 120[/tex]
Since there are 120 children, simply add the number of adults (360 more than this value as mentioned before) and you have your final answer:
[tex]total = 120 + (360 + 120)[/tex]
[tex]total = 600[/tex]
Hope this helped :)
