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?
+129852 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
+237 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
