Question 1204311: I have 5 more brothers than sisters, and each of my brothers have 3 more brothers than sisters. (If there are 10 family members total, how many are brothers)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52855)   (Show Source):
You can put this solution on YOUR website! .
At this forum, there is a nice solution to similar problem, produced years before by our tutors
https://www.algebra.com/algebra/homework/playground/test.faq.question.991197.html
Especially, the solution by the tutor ankor@dixie-net.com has a nice (= a beautiful) idea
on how to start the solution, so you have everything to follow this pattern.
I myself will not write the solution, since the part of the condition
"there are 10 family members total" is ambiguous and admits different interpretations
(including mother, father, grandmother, grandfather etc.). I do not like when
illiterate problems composers turn their problems to soup of words.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website!
I have 5 more brothers than sisters, and each of my brothers have 3 more brothers than sisters. (If there are 10 family members total, how many are brothers)
I do believe that this problem should be edited to read: I have 5 more brothers than sisters, and each of my brothers
have 3 more brothers than sisters. (If there are 10 family members siblings total, how many are brothers) MALES)
Let the number of brothers be B
Then number of sisters = B - 5
Including the NARRATOR, we get the following TOTAL-SIBLINGS equation: 1 + B + B - 5 = 10
2B - 4 = 10
2B = 14
Number of brothers, or 
SCENARIO #1 (MALE NARRATOR)
Now, if a MALE narrator, the number of MALE SIBLINGS = 7 + 1 = 8. This gives us a total of 8 brothers
and 2 sisters, which means that each brother would have 7 brothers and 2 sisters, or 5 more brothers
than sisters. This makes the statement: "each of my brothers have 3 more brothers than sisters," FALSE.
SCENARIO #2 (FEMALE NARRATOR)
Now, if the NARRATOR were FEMALE, and with the established number of brothers being 7 (see above), the number of
FEMALE SIBLINGS would be 3 (2 + narrator). This gives us a total of 7 brothers and 3 sisters, which means that the
narrator (one of the sisters) has 7 brothers and 2 sisters, or 5 more brothers that sisters. This makes the statement:
"I have 5 more brothers than sisters," TRUE.
This also means that each brother would have 6 brothers and 3 sisters, or 3 more brothers than sisters, which also
makes the statement: "each of my brothers have 3 more brothers than sisters," a TRUE one.
Hence, the NARRATOR is FEMALE, and there are 3 FEMALE and 7 MALE SIBLINGS!
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