Ineed some because this problem is tearing my organs !

two times antonio’s age plus three times sarah’s age equals 34. sarah’s age is also five times antonio’s age. how old is sarah?

Let antonio's age = a and let sarah's age = s

2a + 3s = 34 (given in question)
s = 5a (given in question)

Because we know that s = 5a, we can replace it with 5a in the first equation to give this:

2a + 3(5a) = 34
∴ 2a + 15a = 34
∴ 17a = 34
∴ a = 2

Therefore we can see that Antonio is 2. Because we have been told that Sarah is 5 times Antonio's age, we can say that Sarah is 10.