SOLUTION: Mother's age is 4 times as much as the sum of the ages of her three children, but after six years her age will be only double the sum of their ages.The age of the mother is?

Let M be the mother present age.
Let S be the sum of her three children present age.

Then 

M = 4S               (1)     ("Mother's age is 4 times as much as the sum of the ages of her three children")

is your first equation.  

After six eqars, the mother's age will be M + 6.
Each of her three  children's age will be 6 ears more than their present age. 
Hence, the sum of their ages will be 18 years more than the current sum.
It gives you the second equation

M + 6 = 2(S + 18).   (2)     ("after six years her age will be only double the sum of their ages")

To solve the system (1), (2), substitute expression (1) for M into (2). You will get 

4S + 6 = 2S + 36,  or  2S = 30,  or  S =  = 15.

Then

M = 4S = 4*15 = 60.

Mother's present age is 60 years.

Not very realistic, but formally correct.

Let mother's age be M, and sum of children's ages, S

Then we get: M = 4S =====> 

Also, M + 6 = 2(S + 6 * 3)______M + 6 = 2S + 36____M = 2S + 30 ------ eq (ii)

 ---- Substituting  for S in eq (ii)



2M = M + 60 -------- Multiplying by LCD, 2

2M - M = 60 

Mother's age, or