SOLUTION: If 70% of the girls in a class wanted to have a prom and 40% of the boys wanted a prom, is it possible that only 50% of the students in the class wanted a prom? Explain your answer

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Question 245582: If 70% of the girls in a class wanted to have a prom and 40% of the boys wanted a prom, is it possible that only 50% of the students in the class wanted a prom? Explain your answer.
I am lost. Please help, thank you.
Answer by solver91311(24713) About Me  (Show Source):
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If 70% of the girls want a prom and 40% of the boys want a prom, that means that 30% of the girls and 60% of the boys don't want a prom.

In order for the vote to be split 50-50 across the student body the number of students that want the prom, must equal the number of students that don't want the prom, , so:



Combining like terms:





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