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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
edited by SmartMathMan  Jan 11, 2018
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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 :

 

 

 

cool cool cool

 
CPhill  Jan 11, 2018
edited by CPhill  Jan 11, 2018

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