Question 823316
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)