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 years older than his mother and four times the age of his sis

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): You can put this solution on YOUR website!
Equations are solved.
Questions are answered.
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
b,x,m,f
Ben, sister, Mother, Father

-
The two equations involving f:

-

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