Question

The ratio of men to women to children at a concert was 3:5:2. If there were 360 more adults than children, how many people were at the concert?

Answer 1

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 = (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 :)