Final answer:
Sydney's age can be determined by setting up equations based on the information given. By solving these equations, it is found that Sydney is 47 years old.
Step-by-step explanation:
The student is given that Devaughn is 13 years older than Sydney and the sum of their ages is 107. To find Sydney's age, let's denote Sydney's age as S and Devaughn's age as D. According to the information given, we can set up two equations: D = S + 13 and D + S = 107. By substituting the first equation into the second one, we get S + 13 + S = 107. Combining the like terms gives us 2S + 13 = 107. Subtracting 13 from both sides, we get 2S = 94. To find S, divide both sides by 2, resulting in S = 47. Therefore, Sydney's age is 47 years old.