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.
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* 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.
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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.