Two-thirds of the people at a concert are wearing hats. Of those who

don't wear hats, three-fifths wear T-shirts. If the number of people at

the concert without a hat or a T-shirt is 840, then the total number of

people at the concert is?

Guest Apr 1, 2022

#1**+1 **

Call the total number of people at the concert = N

(2/3)N wear hats

Then (1/3)N don't wear hats

And of these, (2/5) don't wear T-shirts, either = (1/3)(2/5)N = (2/15)N

So

(2/15)N = 840

N = (15/2) 840 = 6300 people at the concert

CPhill Apr 1, 2022

#2**+1 **

Let x = number of people

∴ 2/3 (x) = 2x/3 wearing hats

∴ not wearing hats =

x - 2x/3 = (3x - 2x)/3 = x/3, now 3/5 wearing T-shirts, So

x/3 (3/5) = 3x/15, So, not wearing T-shirts, x/3 - 3x/15 = (5x - 3x)/15 = 2x/15, now, 2x/15 = 840

x = 420 (15) = 6300

Total = 6300

Slimesewer Apr 2, 2022