The problem presents pie charts showing the medals won by two teams, Southwell Sports and Fenley Athletics. The pie charts are divided into sections representing bronze, silver, and gold medals, with the angles of each section given. The total number of medals won by each team is also provided. The questions ask to compare the proportion of gold medals for each team, to determine the number of gold medals for each team, and to determine which team won the higher number of gold medals.

1. Problem Description

The problem presents pie charts showing the medals won by two teams, Southwell Sports and Fenley Athletics. The pie charts are divided into sections representing bronze, silver, and gold medals, with the angles of each section given. The total number of medals won by each team is also provided. The questions ask to compare the proportion of gold medals for each team, to determine the number of gold medals for each team, and to determine which team won the higher number of gold medals.

2. Solution Steps

a) Comparing the proportion of gold medals:

First calculate the proportion of gold medals for each team by dividing the angle of the gold section by 360 degrees.

For Southwell Sports, the angle for gold is $192^\circ$.

The proportion of gold medals for Southwell Sports is $\frac{192}{360}$.

For Fenley Athletics, the angle for gold is $180^\circ$.

The proportion of gold medals for Fenley Athletics is $\frac{180}{360}$.

Simplify the fractions:

Southwell Sports: $\frac{192}{360} = \frac{16}{30} = \frac{8}{15} \approx 0.533$

Fenley Athletics: $\frac{180}{360} = \frac{1}{2} = 0.5$

Since $\frac{8}{15} > \frac{1}{2}$, Southwell Sports won the higher proportion of gold medals.

b) Calculate the number of gold medals each team won:

For Southwell Sports, the total number of medals is

7

5. Number of gold medals for Southwell Sports = $\frac{192}{360} \times 75 = \frac{8}{15} \times 75 = 8 \times 5 = 40$

For Fenley Athletics, the total number of medals is

1

2

0. Number of gold medals for Fenley Athletics = $\frac{180}{360} \times 120 = \frac{1}{2} \times 120 = 60$

c) Which team won the higher number of gold medals?

Southwell Sports won 40 gold medals.

Fenley Athletics won 60 gold medals.

Therefore, Fenley Athletics won the higher number of gold medals.

3. Final Answer

a) Southwell Sports

b) Southwell Sports: 40, Fenley Athletics: 60

c) Fenley Athletics