+0  
 
0
117
2
avatar

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?

 Apr 1, 2022
 #1
avatar+124594 
+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

 

 

cool cool cool

 Apr 1, 2022
 #2
avatar+231 
+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

 Apr 2, 2022

30 Online Users

avatar