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# Debate team probs

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One member of the debate team is going to be chosen President. Each member is equally likely to be chosen. The probability that a girl is chosen is 2/3 the probability that a boy is chosen. If the debate team has 20 people, how many girls are there?

May 20, 2019

#1
+8842
+3

Let the number of girls  =  g

Let the number of boys  =  b

b + g  =  20

b  =  20 - g

probability that a girl is chosen  =  $$\frac23$$( probability that a boy is chosen )

$$\frac{g}{20}\,=\,\frac23(\frac{b}{20})\\~\\ \frac{g}{20}\,=\,\frac23(\frac{20-g}{20})\\~\\ g\,=\,\frac23(20-g)\\~\\ \frac32g\,=\,20-g\\~\\ \frac32g+g\,=\,20\\~\\ \frac52g\,=\,20\\~\\ g\,=\,8$$

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May 20, 2019
edited by hectictar  May 20, 2019
edited by hectictar  May 20, 2019
#2
+2551
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Good job Hectitar! I was stumped and now I know how to do this!

CalculatorUser  May 20, 2019
#3
+8842
+2