The problem presents two pie charts showing the medals won by two teams, Holwell Harriers and Dean Runners. The charts display the distribution of bronze, silver, and gold medals for each team, with the total number of medals won by each team also given. The questions ask us to determine which team won a higher *proportion* of gold medals, the exact number of gold medals each team won, and which team won a higher *number* of gold medals.

1. Problem Description

The problem presents two pie charts showing the medals won by two teams, Holwell Harriers and Dean Runners. The charts display the distribution of bronze, silver, and gold medals for each team, with the total number of medals won by each team also given. The questions ask us to determine which team won a higher *proportion* of gold medals, the exact number of gold medals each team won, and which team won a higher *number* of gold medals.

2. Solution Steps

a) Determine which team won the higher *proportion* of gold medals.

For Holwell Harriers:

Total medals = 110

Gold medal angle = $36^\circ$

Proportion of gold medals = $\frac{36}{360} = \frac{1}{10}$

Number of gold medals = $\frac{1}{10} \times 110 = 11$

Proportion of gold medals = $\frac{11}{110} = 0.1$

For Dean Runners:

Total medals = 60

Gold medal angle = $60^\circ$

Proportion of gold medals = $\frac{60}{360} = \frac{1}{6}$

Number of gold medals = $\frac{1}{6} \times 60 = 10$

Proportion of gold medals = $\frac{10}{60} = \frac{1}{6} \approx 0.1667$

Comparing the proportions:

$0.1667 > 0.1$

Therefore, Dean Runners won a higher proportion of gold medals.

b) Work out how many gold medals each team won.

From the previous steps:

Holwell Harriers gold medals = 11

Dean Runners gold medals = 10

c) Determine which team won the higher *number* of gold medals.

From the previous steps, Holwell Harriers won 11 gold medals and Dean Runners won 10 gold medals.

$11 > 10$

Therefore, Holwell Harriers won a higher number of gold medals.

3. Final Answer

a) Dean Runners won the higher proportion of gold medals.

b) Holwell Harriers won 11 gold medals and Dean Runners won 10 gold medals.

c) Holwell Harriers won the higher number of gold medals.