Kate is 48 years older than Stephen. In 15 years time, she will be thrice as old as he. Find Kate's age seven years ago.

Let's denote Stephen's current age as \( S \). Since Kate is 48 years older than Stephen, Kate's current age can be expressed as \( S + 48 \).

In 15 years, Stephen's age will be \( S + 15 \), and Kate's age will be \( S + 48 + 15 = S + 63 \).

According to the problem, in 15 years, Kate's age will be three times Stephen's age:

\[
S + 63 = 3(S + 15)
\]

Now, let's solve this equation:

\[
S + 63 = 3S + 45
\]

Subtract \( S \) from both sides:

\[
63 = 2S + 45
\]

Subtract 45 from both sides:

\[
18 = 2S
\]

Divide both sides by 2:

\[
S = 9
\]

So, Stephen is currently 9 years old, which means Kate's current age is:

\[
S + 48 = 9 + 48 = 57
\]

Finally, to find Kate's age seven years ago:

\[
57 - 7 = 50
\]

Thus, Kate's age seven years ago was **50 years**.

Would you like further details or have any questions?

Here are some related problems you might be interested in:
1. What would be Kate's age 10 years from now?
2. How old will Stephen be in 25 years?
3. What if Kate was 30 years older than Stephen instead of 48?
4. How would the solution change if in 15 years, Kate will be twice as old as Stephen instead of three times?
5. What is the combined age of Kate and Stephen 7 years ago?
6. If Stephen was half Kate's age 10 years ago, how old is Stephen now?
7. How old will Kate be when Stephen turns 30?
8. What is the age difference between Kate and Stephen 20 years ago?

**Tip:** Always verify your solution by substituting the values back into the original problem to ensure accuracy.

Explore how to solve age-related problems involving Kate and Stephen. Understand the method to determine ages based on given conditions with a step-by-step solution example. Suitable for Grades 6-8.

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