Question

trish is 3 times as old as lilly and lilly is twice as old as emma. if the sum of the three girls' ages is 27, how old is emma?

Answer 1

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.