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

Let Sarah's age be s and Antonio's age be a.

According to your question,

2a + 3s = 34
s = 5a

substituting the value of s in eq. 1,

2a + 3(5a) = 34

= 2a + 15 a = 34

17a = 34

thus, a = 34/17 = 2

substituting the value of a is s,

s = 5(2)
= 10

Thus, Sarah's age is 10 years and Antonio's age is 2 years.