Let Emma's age be \( x \).
According to the problem:
- Lilly is twice as old as Emma, so Lilly's age is \( 2x \).
- Trish is three times as old as Lilly, so Trish's age is \( 3(2x) = 6x \).
Now we can express the sum of their ages:
\[ x + 2x + 6x = 27 \]
Combining like terms gives:
\[ 9x = 27 \]
To find Emma's age, divide both sides by 9:
\[ x = \frac{27}{9} = 3 \]
Thus, Emma is \( \boxed{3} \) years old.
To verify, we can find the ages of Lilly and Trish:
- Lilly's age: \( 2x = 2(3) = 6 \)
- Trish's age: \( 6x = 6(3) = 18 \)
Now, check the sum of their ages:
\[ 3 + 6 + 18 = 27 \]
The calculation is correct, confirming that Emma is indeed \( \boxed{3} \) years old.
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