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Let's break down and solve the questions one by one:

---

### **(a) Find the difference between the average crowd attendance for Barcelona and the average crowd attendance for Monaco. Give your answer in standard form.**

From the table:

- Average crowd attendance for **Barcelona**: \( 7.7 \times 10^4 \)
- Average crowd attendance for **Monaco**: \( 9.5 \times 10^3 \)

**Step 1: Subtract the values**
\[
7.7 \times 10^4 - 9.5 \times 10^3 = 77000 - 9500 = 67500
\]

**Step 2: Express the difference in standard form**
\[
67500 = 6.75 \times 10^4
\]

**Answer:** The difference is \( 6.75 \times 10^4 \).

---

### **(b) Is Antonio correct?**
Antonio claims: "The average crowd attendance for Chelsea is approximately 50 times that for Oxford United."

From the table:

- Average crowd attendance for **Chelsea**: \( 4.2 \times 10^4 \)
- Average crowd attendance for **Oxford United**: \( 8.3 \times 10^3 \)

**Step 1: Find the ratio**
\[
\frac{4.2 \times 10^4}{8.3 \times 10^3} = \frac{42000}{8300} \approx 5.06
\]

Antonio claims it's approximately 50 times, but the actual ratio is closer to 5.06, not 50. So **Antonio is incorrect**.

**Answer:** Antonio is incorrect. The average crowd attendance for Chelsea is approximately 5 times, not 50 times, that for Oxford United.

---

### **(c) Work out the overall percentage change in the cost of a ticket to watch Seapron United during last season.**
- First, the cost of a ticket increased by 15%.
- Then, it decreased by 8%.

**Step 1: Let the original price of the ticket be \( P \).**

**Step 2: Apply the 15% increase**
\[
\text{New Price} = P \times 1.15
\]

**Step 3: Apply the 8% decrease to the new price**
\[
\text{Final Price} = (P \times 1.15) \times (1 - 0.08) = P \times 1.15 \times 0.92 = P \times 1.058
\]

**Step 4: Calculate the overall percentage change**
\[
\text{Overall change} = 1.058 - 1 = 0.058
\]

**Answer:** The overall percentage change in the cost of the ticket is a **5.8% increase**.

---

Would you like more details or explanations on any of these solutions? 

Here are five related questions to explore further:
1. How do you calculate percentage increase and decrease in compound steps?
2. What is the importance of using standard form in large number calculations?
3. How do you verify if a claim like Antonio's is valid in real-world contexts?
4. What happens if two percentage changes are applied in reverse (i.e., decrease first)?
5. How do you calculate average ratios in similar comparison problems?

**Tip:** Always convert percentages back to decimals before performing operations like increases or decreases to avoid errors in calculations.

The table gives the average crowd attendance per match for each of five football clubs for one season.
(a) Find the difference between the average crowd attendance for Barcelona and the average crowd attendance for Monaco. Give your answer in standard form.
(b) Antonio says, "The average crowd attendance for Chelsea is approximately 50 times that for Oxford United." Is Antonio correct? You must give a reason for your answer.
(c) During last season the cost of a ticket to watch Seapron United increased by 15% and then decreased by 8%. Work out the overall percentage change in the cost of a ticket to watch Seapron United during last season.

Solve questions involving average crowd attendance in standard form, validating ratio claims, and calculating overall percentage change in ticket prices. Includes step-by-step solutions on how to find differences, ratios, and percentage changes. Suitable for students in Grades 9-11.

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