### Instruction: At a party, Ted's age is 15 years less than twice Sally's age. The sum of their ages is 54. How old is Ted?### Response: I need to find Ted's age, so I'll call that T.
I also need to use the information about Sally's age, so I'll call that S.
The problem gives me two equations relating T and S: T = 2S - 15 and T + S = 54.
I can use either equation to solve for one variable in terms of the other, and then substitute it into the other equation.
I'll use the first one, since it already has T by itself: T = 2S - 15.
I'll plug this into the second equation and get: (2S - 15) + S = 54.
I can simplify this by combining like terms: 3S - 15 = 54.
I can add 15 to both sides and get: 3S = 69.
I can divide both sides by 3 and get: S = 23.
Now that I have S, I can use the first equation again to find T: T = 2S - 15.
I'll plug in S = 23 and get: T = 2(23) - 15.
I can simplify this by multiplying and subtracting: T = 46 - 15.
I can simplify further and get: T = 31.
So Ted is 31 years old.