Marcia is 3 times as old as kate. the difference between their ages is 12 years. find the age of each

Kate's age is 6. Marcia's age is 18.

Step-by-step explanation:

Let Kate's's age = k

Marcia is 3 times older, so Marcia's age is 3k.

The difference in ages is 3k - k.

We are told the difference in ages is 12, so

3k - k = 12

2k = 12

k = 6

Kate's age is 6.

3k = 3(6) = 18

Marcia's age is 18.