Posted by Nina on Saturday, April 17, 2010 at 11:21pm.
Here is a similar version of this popular problem which should give you some clues as to how to approach yous.
In a family of children,
1) each girl has as many bothers as sisters but
2) each boy has 3 times as many sisters as brothers.
How many children are in the family?
Let g = the number of girls
Let b = the number of boys
1--Looking at the girls only, it is clear that each girl has one less as many sisters as there are girls in the first place.
2--Therefore, we can write that each girl has (g - 1) sisters.
3--From statement #1, if each girl has as many brothers as sisters, we can write that (g - 1) = b.
4--Similarly, we know that each boy has (b - 1) brothers and g sisters.
5--From statement #2, if each boy has 3 times as many sisters as brothers, we can write that g = 3(b - 1) = 3b - 3.
6--Substituting (5) into (3) yields 3b - 3 - 1 = b.
7--Then, 2b = 4 making b = 2 and g = 3.
Good luck.
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