On a rainy day, every kid at Margo's school brings a raincoat, an umbrella, or both. 8% of the kids bring both. The total number of kids with umbrellas is twice the total number of kids with raincoats.
What percent of the kids bring ONLY an umbrella?
Let the number of students be arbitrarily set at 100
Let the number of kids who bring only an umbrella = U and let the number who bring only a raincoat = R
U + 8 + R = 100 ⇒ U + R = 92 ⇒ U = 92 - R (1)
And the number that bring umbrellas is twice that of those who bring raincoats..so....
(U + 8) = 2 (R + 8) (2) sub (1) into (2)
(92 - R + 8) = 2(R + 8)
100 - R = 2R + 16
84 = 3R
28% = R ⇒ % who bring only a raincoat
So....92 - 28 = 64% bring only an umbrella
Here's a Venn diagram :