Start by assigning variables. It is best, if possible, to then write each of the variables in terms of 1 variable (preferably the one you seek).
Let A be Adam's age, B be Ben's age, and C be Caroline's age.
Since A is Adam's age, A=A.
Since Ben is twice as old as Adam, B=2A. (Twice indicates multiplication by 2)
Since Caroline is 7 years older than Adam then C=A+7.
The sum of the ages is 27 so:
A+(2A)+(A+7)=27. Now collect like terms:
4A+7=27 Subtract 7 from both sides
4A=20 Dicide both sides by 4 (Multiply both sides by 1/4 if you prefer)
Thus Adam is 5; this makes Ben 2(5)=10 and Caroline 5+7=12.
The three ages are Adam is 5 yrs, Ben is 10 yrs, and Caroline is 12 yrs.
** Checking we see that 5+10+12=27 and 10=2(5) and 12=5+7 as required. **