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 Pick-a-book meeting (Posted on 2018-02-12)
At a meeting of the Young Historical Society (YHS) in a local library the number of children present was three times the number of parents.
At this meeting, each boy borrowed 12 books from the library, each girl borrowed 17 books and each parent borrowed 9 books.
In total 305 books were borrowed.

How many girls were there at the YHS meeting?

 See The Solution Submitted by Ady TZIDON No Rating

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 Solution | Comment 1 of 5
Start by finding the number of parents
p=parents, 3p=kids
The kid's average number of books is in the range {12to17}
p*9+3p{12to17}=305
Using 12 gives p=6.778
Using 17 gives p=5.083
p is a whole number in between these values, so p=6 and there are 18 kids who got the remaining 305-6*9=251 books.

If they were all boys they would only have gotten 18*12=216

Need to make up the other 251-216=35.
Each girl gets 5 more books than boys.  35/5=7.
So there are 7 girls, 11 boys, and 6 parents.

 Posted by Jer on 2018-02-12 09:20:12

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