The image shows pie charts representing the medals won by two teams, City Athletics and Teignford Track. The problem asks us to determine which team won the higher proportion of silver medals, calculate the number of silver medals each team won, and determine which team won the higher number of silver medals.

1. Problem Description

The image shows pie charts representing the medals won by two teams, City Athletics and Teignford Track. The problem asks us to determine which team won the higher proportion of silver medals, calculate the number of silver medals each team won, and determine which team won the higher number of silver medals.

2. Solution Steps

a) To determine which team won the higher proportion of silver medals, we need to calculate the proportion of silver medals for each team. The proportion is the number of degrees allocated to silver medals divided by 360 degrees.

For City Athletics, the angle for silver medals is 132 degrees. So, the proportion of silver medals is $\frac{132}{360}$.

For Teignford Track, the angle for silver medals is 108 degrees. So, the proportion of silver medals is $\frac{108}{360}$.

Comparing these proportions:

$\frac{132}{360} = \frac{11}{30} \approx 0.3667$

$\frac{108}{360} = \frac{3}{10} = 0.3$

Since $\frac{132}{360} > \frac{108}{360}$, City Athletics won a higher proportion of silver medals.

b) To work out how many silver medals each team won, we multiply the proportion of silver medals by the total number of medals won by each team.

For City Athletics, the total number of medals won is

9

0. The number of silver medals is $\frac{132}{360} \times 90 = \frac{11}{30} \times 90 = 11 \times 3 = 33$ silver medals.

For Teignford Track, the total number of medals won is

1

4

0. The number of silver medals is $\frac{108}{360} \times 140 = \frac{3}{10} \times 140 = 3 \times 14 = 42$ silver medals.

c) To determine which team won the higher number of silver medals, we compare the number of silver medals each team won.

City Athletics won 33 silver medals.

Teignford Track won 42 silver medals.

Since 42 > 33, Teignford Track won the higher number of silver medals.

3. Final Answer

a) City Athletics won the higher proportion of silver medals.

b) City Athletics won 33 silver medals, and Teignford Track won 42 silver medals.

c) Teignford Track won the higher number of silver medals.