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.
\(4:1 = (x+360) : x\)
Cross-multiply the two ratios to get the expression below, simplify and solve for x:
\(x + 360 = 4x\)
\(360 = 4x - x\)
\(360 = 3x\)
\(x = \frac{360}{3}\)
\(x = 120\)
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:
\(total = 120 + (360 + 120)\)
\(total = 600\)
Hope this helped :)
