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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? Explain your solution in complete sentences.

 Jan 5, 2019
 #1
avatar+5788 
+1

you're gonna have to translate this to complete sentences

 

\(\text{let }N \text{ be the total number of kids}\\ R \text{ is the set of kids that bring raincoats}\\ U \text{ is the set of kids that bring umbrellas}\\ |U|=2|R|\\ |U\cap R|=0.08N\)

 

\(N = |U \cup R| = |U| + |R| - |U \cap R|\\ N = |U|+\dfrac{|U|}{2} - 0.08 N\\ 0.92N = \dfrac 3 2 |U|\\ |U| = \dfrac 2 3 0.92 N = \dfrac{184}{300}N\)

 

\(|\text{kids that only bring umbrellas}| = |U| - |U\cap R| = \\ \dfrac{184}{300}N - \dfrac{8}{100}N = \dfrac{160}{300}N = \dfrac{8}{15}N\\ \dfrac{8}{15} \approx 53.3\%\)

.
 Jan 5, 2019
 #2
avatar+103131 
+4

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?

 

For simplicity, let's suppose that there are 100 kids at the school

If 8% bring both, then 8 bring both

Let the number who bring raincoats = x

Let the number who bring umbrellas =  2x

So....the ones that bring only raincoats = x - 8

And the ones that bring only umbrellas = 2x - 8

So......we have this equation

 

Kids who bring only umbrellas + kids who bring both + kids who only bring raincoats = 100

(2x -8)  +  8  + (x - 8)  =  100      simplify

3x - 8   = 100      add 8 to both sides

3x = 108      divide both sides by 3

x = 36

So....the ones who bring only a rain coat =  36 - 8  =  28

 

And the ones who bring only an umbrella  = 2(36) - 8  =  72 - 8  = 64 = 64%

 

Check

Only umbrellas +  Both + Only Raincoats = 100  ???

64  +  8  +  28   =  100   (Check)

 

cool cool cool

 Jan 5, 2019

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