SOLUTION: A mother is 8 times as old as her daughter and 4 times as old as her son. How old is each if the son is 4 years older than the daughter?

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Question 333436: A mother is 8 times as old as her daughter and 4 times as old as her son. How old is each if the son is 4 years older than the daughter?
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let m = Mother's age
Let d = Daughter's age
Let s = Son's age
given:
m+=+8d
m+=+4s
s+=+d+%2B+4
This is 3 equations and 3 unknowns, so it's solvable
By substitution:
m+=+4%2A%28d+%2B+4%29
m+=+4d+%2B+16
Again, by substitution:
8d+=+4d+%2B+16
4d+=+16
d+=+4
and, since,
m+=+8d
m+=+8%2A4
m+=+32
also,
s+=+d+%2B+4
s+=+4+%2B+4
s+=+8
The Mother is 32, the Daughter is 4, and the Son is 8

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A mother is 8 times as old as her daughter and 4 times as old as her son.
m = 8d
m = 4s
:
How old is each if the son is 4 years older than the daughter?
s = d + 4
:
replace s with (d+4) in the equation m = 4s
m = 4(d+4)
m = 4d + 16
Replace m with 8d from the 1st equation
8d = 4d + 16
8d - 4d = 16
4d = 16
d = 4 yrs is the daughter's age
:
We know that s = d+4, therefore
s = 4 + 4
s = 8 yrs son's age
then
m = 4s
m = 4(8)
m = 32 yrs is Mom's age
:
;
summarize; Mom is 32, son is 8, daughter is 4