SOLUTION: There are a certain amount of books. If we give these books only to the girls in the class, every girl gets 15 books. If we give those same books to the boys in the class, each b

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Question 847163: There are a certain amount of books. If we give these books only to the girls in the class, every girl gets 15 books. If we give those same books to the boys in the class, each boy gets 10 books. If we give these books to everyone in the class, how many books can each student get? I figured out the ratio of boys to girls (3:2) but I am very confused about the rest. Thank you for the help if you can!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = number of girls
Let +b+ = number of boys
--------------------------
+15g+=+10b+
The numbers that make this true are:
+g+=+10n+ and
+b+=+15n+ where +n+ is any whole number
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The total number of books is +10b+
I want to divide this number by +g+%2B+b+
--------------------------------------
+%28+10%2A15n+%29+%2F+%28+10n+%2B+15n+%29+
+%28n%2Fn%29%2A%28%28+150+%29+%2F++%28+25+%29%29+=+6+
Each student gets 6 books
check:
+6%2A%28+g+%2B+b+%29+=+10b+
+6g+%2B+6b++=+10b+
+4b+=+6g+
+g%2Fb+=+2%2F3+
OK
There may be a more direct way of solving this
I just kind of followed my own logic