In a recent wedding, the groom's age was fifteen years more than half the bride's age. If the sum of their ages was 51 years, how old was the groom?
Let the groom's age be $g$ and the bride's age be $b$. We are trying to find the value of $g$. We can write a system of two equations to represent the given information. Here are our two equations: \begin{align*}
g &= \frac{1}{2}b + 15 \\
g + b &= 51.
\end{align*} The first equation represents the statement ``the groom's age was fifteen years more than half the bride's age.'' The second equation represents the statement ``if the sum of their ages was 51 years...'' We are solving for $g$, so we want to eliminate $b$. From the second equation, we get that $b=51-g$. Substituting that into the first equation to get rid of $b$, we have $g=\frac{1}{2}(51-g)+15$, from which we get that $g=27$. Thus, the groom's age is $\boxed{27}$ years old.