Billy's age is twice Joe's age and the sum of their ages is 45. How old is Billy?
To find Billy's age, I need to find a way to relate it to Joe's age using the given information. I notice that the problem says Billy's age is twice Joe's age, so I can write an equation for that: B = 2J, where B is Billy's age and J is Joe's age. I also notice that the problem says the sum of their ages is 45, so I can write another equation for that: B + J = 45. Now I have a system of two equations with two variables, and I can use substitution to solve it. Since I already know that B = 2J, I can plug that into the second equation and get: 2J + J = 45. This simplifies to 3J = 45, so I can divide both sides by 3 and get: J = 15. This means Joe is 15 years old, but I still need to find Billy's age. To do that, I can use the first equation again and substitute J = 15: B = 2J = 2(15) = 30. This means Billy is 30 years old, and that's my final answer. 