Sibling rivalry: How many boys and girls in the family?

pianoplaya16

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Sammy and Susie are siblings. Sammy has as many brothers as sisters. Susie has twice as many brothers as sisters. How many boys and girls are there in the family?
 
That's a lovely problem. What have you tried.

Normally, It is good to write down defintions of the items in the problem statement that are not defined for you.
 
pianoplaya16 said:
Sammy and Susie are siblings. Sammy has as many brothers as sisters. Susie has twice as many brothers as sisters. How many boys and girls are there in the family?
This oldie should give you a clue as to soving your problem.

Jennifer's family has fewer than than ten children. She has the same number sisters as she has brothers, but her brother Mike has twice as many sisters as he has brothers. How many girls are in the family?

There are G girls and B boys.

Since Jennifer has the same number of sisters as she does brothers, the number of girls G = B + 1 making G - B = 1.

Since Mike has twice as many sisters as he does brothers, G = 2(B - 1) or 2B - G = 2.

Adding 2B - G = 2 and
...........-B + G = 1
............B = 3 making G = 4.
 
Hello, pianoplaya16!

Sammy and Susie are siblings.
Sammy has as many brothers as sisters.
Susie has twice as many brothers as sisters.
How many boys and girls are there in the family?

Make a sketch . . .

\(\displaystyle \underbrace{b\:b\:b\:\cdots\:b}_{B\text{ boys}}\;\;\underbrace{g\:g\:g\:\cdots\:g}_{G\text{ girls}}\)


Sammy has as many brothers as sisters.
. . \(\displaystyle \fbox{Sammy}\:\underbrace{b\:b\:\cdots\;b}_{B-1\text{ brothers}}\;\;\underbrace{g\:g\:g\:\cdots\:g}_{G\text{ sisters}}\)

. . Hence, we have: \(\displaystyle \:B\,-\,1\:=\:G\;\;\Rightarrow\;\;B\,-\,G\:=\:1\;\) [1]


Susie has twice as many brothers as sisters.
. . \(\displaystyle \underbrace{b\:b\:b\:\cdots\:b}_{B\text{ brothers}}\;\;\fbox{Susie}\:\underbrace{g\;g\;\cdots\;g}_{G-1\text{ sisters}}\)

. . Hence, we have: \(\displaystyle B \:=\:2(G\,-\,1)\;\;\Rightarrow\;\;B\,-\,2G\:=\:-2\;\) [2]


Subtract [2] from [1]: \(\displaystyle \:G\:=\:3\)

Substitute into [1]: \(\displaystyle \:B\,-\,3\:=\:1\;\;\Rightarrow\;\;B \,=\,4\)


Therefore, there are 4 boys and 3 girls in the family.

 
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