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Let's analyze the given problem step by step.

We are provided with two teams, Howell Harriers and Dean Runners, and a pie chart showing the proportions of medals won (Gold, Silver, and Bronze) by each team. The total number of medals won by Howell Harriers is 110, and the total number of medals won by Dean Runners is 60.

### Part (a) - Which team won the higher proportion of gold medals?

From the chart, we observe:
- **Howell Harriers**: The gold section is 144°, and the total circle is 360°. The proportion of gold medals is:
  \[
  \text{Proportion of Gold Medals for Howell Harriers} = \frac{144^\circ}{360^\circ} = 0.4 \text{ (or } 40\%).
  \]
- **Dean Runners**: The gold section is 192°, and the total circle is 360°. The proportion of gold medals is:
  \[
  \text{Proportion of Gold Medals for Dean Runners} = \frac{192^\circ}{360^\circ} = 0.5333 \text{ (or } 53.33\%).
  \]

Thus, **Dean Runners** won a higher proportion of gold medals.

### Part (b) - Work out how many gold medals each team won.

Now, we'll calculate the actual number of gold medals won by each team.

- **Howell Harriers**: 
  \[
  \text{Number of Gold Medals} = 0.4 \times 110 = 44 \text{ gold medals}.
  \]

- **Dean Runners**:
  \[
  \text{Number of Gold Medals} = 0.5333 \times 60 = 32 \text{ gold medals}.
  \]

### Part (c) - Which team won the higher number of gold medals?

From part (b), Howell Harriers won **44 gold medals**, and Dean Runners won **32 gold medals**. Therefore, **Howell Harriers** won the higher number of gold medals.

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Do you need any further details or clarification on the calculations?

Here are 5 follow-up questions to consider:
1. How would you calculate the total number of silver medals for each team?
2. What is the difference in the total number of medals won by the two teams?
3. How would you compute the proportion of bronze medals for each team?
4. How do the proportions of silver medals compare between the two teams?
5. Can you calculate the combined proportion of gold medals won by both teams?

**Tip:** To calculate proportions from pie charts, always divide the angle of the section by 360° to get the proportion, then multiply by the total quantity represented.

The medals won by two teams in a competition are shown in a pie chart. a) Which team won the higher proportion of gold medals? b) Work out how many gold medals each team won. c) Which team won the higher number of gold medals?

Solve the problem of calculating the proportion and number of gold medals won by two teams from a pie chart. This problem covers key math concepts, such as proportions and working with angles in a circle, suitable for students in Grades 6-8.

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