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)

A=5

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. **