Kate is six years younger than Bob.Twelve years ago,Bob was twice as old as Kate was then.
How old are they both now?
K+6=B
K-12=B/2
subtract the equations
18=B/2
B=36
K=30
To find the current age of Kate and Bob, let's first assign variables to their ages.
Let's assume Bob's current age is x.
Therefore, Kate's current age would be x - 6, as Kate is six years younger than Bob.
Now, let's use the information given about twelve years ago.
Twelve years ago, Bob's age would have been x - 12, and Kate's age would have been (x - 6) - 12, which simplifies to x - 18.
According to the problem, twelve years ago, Bob's age was twice Kate's age:
x - 12 = 2(x - 18)
Now we can solve the equation to find the value of x, which represents Bob's current age.
x - 12 = 2x - 36 (expand the parentheses)
x - 2x = -36 + 12 (subtract x from both sides)
-x = -24 (combine like terms)
x = 24 (multiply both sides by -1, which changes the sign)
Therefore, Bob's current age is 24 years.
Now, we can find Kate's current age using her relationship with Bob:
Kate's current age = Bob's current age - 6
Kate's current age = 24 - 6
Kate's current age = 18 years
So, Bob is currently 24 years old, and Kate is currently 18 years old.