Question 245582
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If 70% of the girls <b><i>want</i></b> a prom and 40% of the boys <b><i>want</i></b> a prom, that means that 30% of the girls and 60% of the boys <b><i>don't want</i></b> a prom.


In order for the vote to be split 50-50 across the student body the number of students that want the prom, *[tex \Large .7g\ +\ .4b] must equal the number of students that don't want the prom, *[tex \Large .3g\ +\ .6b], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ .7g\ +\ .4b\ =\ .3g\ +\ .6b]


Combining like terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ .4g\ =\ .2b]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2g\ =\ b]


So as long as you have at least 10 girl students and the number of girl students is a multiple of 10 (so that you don't have a fractional part of a girl when you calculate 70% of them) and twice as many boys as you have girls, you will have exactly 50% of the students that want the prom and 50% that don't given 70% girls and 40% boys want the prom.


Try it:


10 girls X 70% = 7, X 30% = 3

20 boys X 40% = 8, X 60% = 12

30 students X 50% = 15 and 8 + 7 = 15 and 3 + 12 = 15



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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