Amelia is 10 years older than 3 times taylors age. how old is amelia if the sum of their ages is 30

Let x be the age of Amelia, and y the age of Taylor.


We can simplify the second equation to get:


We can solve for x in the first equation to get:
 
Now we can replace this into our second equation to get:





Now know that the age of Taylor is 5 years, let's find the age of Amelia replacing this value into our equation  


We conclude that the age of Amelia is 25 year old and Taylor is 5 years old.