SOLUTION: Please solve this question, Ben is 3 years older than his sister and a third of the age of his mother. His father is 4 year older than his mother and four time the age of his sis

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please solve this question, Ben is 3 years older than his sister and a third of the age of his mother. His father is 4 year older than his mother and four time the age of his sis      Log On


   

Question 1099307: Please solve this question,
Ben is 3 years older than his sister and a third of the age of his mother.
His father is 4 year older than his mother and four time the age of his sister.
How old is Ben ?
Regards
Raza
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
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From the condition, you have

B = S + 3,

3B = M,

F = M + 4,

4S = F.


Then moving from the bottom to the top and making substitutions, you get this chain of equalities

4S = F = M + 4 = 3B + 4 = 3*(S+3) + 4.


which gives you 

4S = 3*(S+3) + 4 ====>  4S = 3S + 13  ====>  S= 13.


The sister is 13 years old.  Ben is 13 + 3 = 16 years old.


The mother is  3*16 = 48 years old  and the father is  52 years old.

Solved.