Question

Rowena is now half as her mother. 8 years ago, she was 1/3 as old. Find their ages.

So is the half 1/2x or x/2?

Answer 1

same thing

e.g. (1/2)(12) = 6
12/2 = 6

as to your question,
mom's age ---- x
Rowena's age -- x/2

8 years ago:
mom ---- x-8
Rowena -- x/2 - 8

x/2 - 8 = (1/3)(x-8)
times 6, the LCD
3x - 48 = 2(x-8)
3x - 48 = 2x - 16
x = 32

Mom is 32, Rowena is 16

check:
8 years ago, the mom was 24
Rowena was 8, which is 1/3 of 24

(mmmhh, so Mom had Rowena when she was 16 ? Not a suitable question.)

Answer 2

same thing

e.g. (1/2)(12) = 6
12/2 = 6

as to your question,
mom's age ---- x
Rowena's age -- x/2

8 years ago:
mom ---- x-8
Rowena -- x/2 - 8

x/2 - 8 = (1/3)(x-8)
times 6, the LCD
3x - 48 = 2(x-8)
3x - 48 = 2x - 16
x = 32

Mom is 32, Rowena is 16

check:
8 years ago, the mom was 24
Rowena was 8, which is 1/3 of 24