SOLUTION: Currently, my father's age is four times the total age of my sister and me, but eight years from now, it will be only double. Also, in three years, my age will be twice my sister's

Question 823316: Currently, my father's age is four times the total age of my sister and me, but eight years from now, it will be only double. Also, in three years, my age will be twice my sister's age. What is the current age of my father, my sister, and me?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
f = father's present age; b = brother's age; s = sisters age
:
Currently, my father's age is four times the total age of my sister and me,
f = 4(b + s)
f = 4b + 4s
:
but eight years from now, it will be only double.
f + 8 = 2(b+8 + s+8)
f + 8 = 2(b+s+16)
f + 8 = 2b + 2s + 32
f = 2b + 2s + 32 - 8
f = 2b + 2s + 24
f = f so we can write it
4b + 4s = 2b + 2s + 24
combine like terms
2b + 2s = 24
:
Also, in three years, my age will be twice my sister's age.
b + 3 = 2(s+3)
b + 2 = 2s + 6
b = 2s + 6 - 3
b = 2s + 3
b - 2s = 3
Use elimination with these two equations
2b + 2s = 24
b - 2s = 3
--------------adding eliminates s find b
3b = 27
b = 27/3
b = 9 yrs is the brothers age
find s using 2b + 2s = 24
2(9) + 2s = 24
2s = 24 - 18
2s = 6
s = 3 yrs is sisters age
then
f = 4(9 + 3)
f = 48 yrs is dad's age
:
:
Check solutions in the statement:
"eight years from now, it will be only double.
48 + 8 = 2(9+8 + 3+8)
56 = 2(17+11)
56 = 2(28)
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