https://file.aiquickdraw.com/mathbot/file/17298019282765s9aigqu.jpg

Let's break down and solve the questions in the image:

### Part (a):
The mean age of five tennis players is given as 24 years.

This means the total sum of the ages of all five players is:
\[
\frac{\text{Sum of ages of five players}}{5} = 24
\]
So, the total sum of their ages is:
\[
\text{Sum of ages of five players} = 24 \times 5 = 120 \text{ years}.
\]

Now, we are told the mean age of four of them is 23 years. This implies:
\[
\frac{\text{Sum of ages of four players}}{4} = 23
\]
So, the total sum of their ages is:
\[
\text{Sum of ages of four players} = 23 \times 4 = 92 \text{ years}.
\]

To find the age of the fifth player, we subtract the sum of the four players' ages from the total sum of the five players' ages:
\[
\text{Age of the fifth player} = 120 - 92 = 28 \text{ years}.
\]

### Part (b):
Now, we need to find the mean age of these players after 3 years. In 3 years, each player will age by 3 years, so their total age will increase by \(5 \times 3 = 15\) years.

Thus, the new total age of the five players after 3 years will be:
\[
120 + 15 = 135 \text{ years}.
\]

The new mean age will be:
\[
\frac{135}{5} = 27 \text{ years}.
\]

### Summary:
(a) The age of the fifth player is **28 years**.
(b) The mean age of the players after 3 years will be **27 years**.

Would you like further details or explanations?

Here are 5 related questions to expand your understanding:
1. How would the answer change if the mean age of the four players was 22 years instead of 23?
2. What if there were 6 players with the same mean age of 24 years?
3. How would the mean age be affected if only 2 years passed instead of 3?
4. Can you express the age of the fifth player as a variable and generalize the solution?
5. How would the problem change if only the median age were provided instead of the mean?

**Tip**: The mean is sensitive to extreme values, whereas the median provides more resistance to outliers. Always consider which measure is more appropriate for your data!

The mean age of five tennis players is 24 years. (a) If the mean age of four of them is 23 years, find the age of the fifth player. (b) Find the mean age of these players after 3 years.

Solve the problem of determining the age of the fifth tennis player given the mean age of four and the total group. This exercise covers the concept of averages and finding future mean ages. Suitable for Grades 6-8.

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