Question 1118700: 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 years older than his mother and four times the age of his sister. How old is Ben ? ---------
Regards
Found 4 solutions by Theo, MathTherapy, Alan3354, josgarithmetic:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! b = ben's age.
f = ben's father's age.
m = ben's mother's age.
s = ben's sister's age.
ben is 3 years older than his sister leads to b = s + 3.
ben is 1/3 the age of his mother leads to b = 1/3 * m.
ben's father is 4 years old than his mother leads to f = m + 4.
ben's father is 4 times the age of ben's sister leads to f = 4 * s.
you have 4 equations that need to be solved simultaneously.
they are:
b = s + 3
b = 1/3 * m
f = m + 4
f = 4 * s
from f = m + 4 and f = 4 * s, you get m + 4 = 4 * s.
solve for m to get m = 4 * s - 4.
from b = s + 3 and b = 1/3 * m, you get s + 3 = 1/3 * m.
solve for m to get m = 3 * s + 9.
from m = 4 * s - 4 and m = 3 * s + 9, you get 4 * s - 4 = 3 * s + 9.
solve for s to get s = 13.
from b = s + 3, replace s with 13 to get b = 13 + 3 which results in b = 16.
from f = 4 * s, replace s with 13 to get f = 4 * 13 which results in f = 52.
from f = m + 4, replace f with 52 and solve for m to get m = 48.
you now have:
s = 13
b = 16
f = 52
m = 48
b = s + 3 becomes 16 = 13 + 3 which is true.
b = 1/3 * m becomes 16 = 1/3 * 48 which is true.
f = m + 4 becomes 52 = 48 + 4 which is true.
f = 4 * s becomes 52 = 4 * 13 which is true.
all statements are true, so the solution looks good.
the solution is:
ben's age is 16.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! 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 years older than his mother and four times the age of his sister. How old is Ben ? ---------
Regards
Let Ben’s age be B
Then sister's age is: B – 3, and mother’s is: 3B
Father's is: 3B + 4, and also, 4(B – 3), or 4B - 12
We then have: 3B + 4 = 4B – 12
3B – 4B = - 12 – 4
- B = - 16
B, or Ben is: 
Answer by Alan3354(69443)  (Show Source):
Answer by josgarithmetic(39625)  (Show Source):
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