Cersei is 3 times older than arya. in 15 years their combined ages will be 94.how old are each of them now ( show work)

The "work" can be all in your head. In 15 years, their combined ages will have increased by 30 years over what it is now*, so their combined age now must be 64 year. If the ratio of their ages is 3:1, the youngest must be 1/(3+1) = 1/4 of the total, or 16 years.

Arya is 16 years old; Cersei is 48 years old.

* Each person ages one year each year, so their combined age increases by 2 years each year. In 15 years, their combined age will increase by 30 years.

If you insist on an equation, let "a' represent Arya's age. Then 3a represents Cersei's age. The relationship given in the problem is ...

... (a +15) + (3a +15) = 94

... 4a +30 = 94 . . . . . . . . . . collect terms

... 4a = 64 . . . . . . . . . . . . . . subtract 30

... a = 64/4 = 16 . . . . . . . . . multiply by 1/4

This equation and its working should look a lot like the verbal reasoning we did above.

$12. that is my answer.