jmc

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: $$\begin{array}{rl}g& =\frac{1}{2}b+15\\ g+b& =51.\end{array}$$ 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.