### Instruction: 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?### Response: This problem involves finding the ages of two people, the groom and the bride, based on a relationship between them and the sum of their ages.
I can use algebra to set up a system of equations that represents this situation.
Let x be the groom's age and y be the bride's age.
Then the first equation is x = 15 + y/2, which means the groom's age is fifteen years more than half the bride's age.
The second equation is x + y = 51, which means the sum of their ages is 51 years.
To solve this system, I can substitute x from the first equation into the second equation, and get 15 + y/2 + y = 51.
Simplifying this equation, I get y/2 + y = 36, or 3y/2 = 36.
Multiplying both sides by 2/3, I get y = 24, which means the bride is 24 years old.