SOLUTION: in a family mother's age is twice that of daughters age father is 10 years older than mother. brother is 20 years younger than mother and 5 years older than his sister. what is fat

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Question 556802: in a family mother's age is twice that of daughters age father is 10 years older than mother. brother is 20 years younger than mother and 5 years older than his sister. what is fathers age.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let f = father's age
Let m = mother's age
Let d = daughter's (sister) age
Let s = son's (brother) age
:
Write an equation for each statement
:
"mother's age is twice that of daughters age"
m = 2d
:
"father is 10 years older than mother."
f = m + 10
:
rearrange the next two equations for elimination.
"brother is 20 years younger than mother"
s = m - 20
replace m with 2d and you have
s = 2d - 20
s - 2d = -20
multiply by -1
-s + 2d = 20
:
"and 5 years older than his sister. "
s = d + 5
s - d = 5
;
Use these two equation for elimination
-s + 2d = 20
s - d = 5
--------------addition eliminates s, find d
d = 25 is daughter's age
:
we know m = 2d
m = 2(25)
m = 50 yrs is Mom's age
then
f = m + 10
f = 50 + 10
f = 60 yrs is father's age, which is what they want