A dad is now three times as old as his son, but in eleven years the dad will be only two times as old as his son is then. How old will the dad be next year?
To find the current age of the dad, we can set up a system of equations based on the information given.
Let's say the son's current age is x.
According to the problem, the dad is now three times as old as his son, so the dad's current age is 3x.
In eleven years, the dad will be two times as old as his son is then, so we can represent the dad's age in eleven years as 3x + 11, and the son's age in eleven years as x + 11.
Setting up the equation:
3x + 11 = 2(x + 11)
Let's solve for x:
3x + 11 = 2x + 22
Subtract 2x from both sides:
x + 11 = 22
Subtract 11 from both sides:
x = 11
Now that we know the son's current age is 11, we can find the dad's current age:
Dad's current age = 3x = 3(11) = 33
To find the dad's age next year, we simply add 1 to his current age:
Dad's age next year = 33 + 1 = 34
Therefore, the dad will be 34 years old next year.