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:

$x + 360 = 4x$
$360 = 4x - x$
$360 = 3x$
$x = \frac{360}{3}$
$x = 120$

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 :)