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?

SmartMathMan
Jan 11, 2018

#1**+1 **

Let's see......

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

So

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 :

CPhill
Jan 11, 2018