Question

the average of amy's, ben's, and chris's ages is 6. four years ago, chris was the same age as amy is now. in four years, ben's age will be of amy's age at that time. how many years old is chris now?

Answer 1

Amy is 6, Ben is 9, and Chris is 3 years old.

Step-by-step explanation:

Let's represent Amy's age as 'a', Ben's age as 'b', and Chris's age as 'c'.

The average of their ages is given as 6, so we can write the equation: (a + b + c) / 3 = 6.

Four years ago, Chris was the same age as Amy is now. We can write this as: c-4 = a.

In four years, Ben's age will be (b+4) and Amy's age will be (a+4). We are told that Ben's age at that time will be half of Amy's age at that time. We can write this as: b+4 = (1/2)*(a+4).

We can use these equations to solve for their ages. Solving the first equation, we get: a + b + c = 18. Substituting 'a' with 'c-4' in the second equation, we get: c-4 + b + c = 18. Simplifying, we get: 2c + b - 4 = 18. Substituting 'b' with '(1/2)*(a+4)' in the third equation, we get: (1/2)*(a+4) + 4 = (a+4).

Solving these equations, we find that a = 6, b = 9, and c = 3. Therefore, Chris is currently 3 years old.