Question

Kevin is two times as old as Bob. Three years ago the sum of their ages was 18. How old is each​ now?

Answer 1

Let's denote Kevin's current age as \( K \) and Bob's current age as \( B \).

From the problem, we have the following two equations:

1. \( K = 2B \) (Kevin is two times as old as Bob)
2. \( (K - 3) + (B - 3) = 18 \) (Three years ago, the sum of their ages was 18)

We can simplify the second equation:

\[
K - 3 + B - 3 = 18
\]
\[
K + B - 6 = 18
\]
\[
K + B = 24
\]

Now, we have a system of equations:
1. \( K = 2B \)
2. \( K + B = 24 \)

We can substitute the first equation into the second equation:

\[
2B + B = 24
\]
\[
3B = 24
\]
\[
B = 8
\]

Now that we have Bob's age, we can find Kevin's age:

\[
K = 2B = 2 \times 8 = 16
\]

So, Kevin is currently 16 years old and Bob is currently 8 years old.

**In conclusion:**
- Kevin's age: 16
- Bob's age: 8