The problem shows pie charts representing the medals won by two teams, Hamstead Harriers and Ebford Athletics. We need to determine which team won the higher proportion of silver medals and then calculate the number of silver medals for each team.

1. Problem Description

The problem shows pie charts representing the medals won by two teams, Hamstead Harriers and Ebford Athletics. We need to determine which team won the higher proportion of silver medals and then calculate the number of silver medals for each team.

2. Solution Steps

a) Comparing Proportions of Silver Medals

First, we need to find the proportion of silver medals for each team. The proportion is the angle representing silver divided by 360 degrees.

For Hamstead Harriers:

Angle for silver = $129^{\circ}$

Total medals = 120

Proportion of silver medals = $\frac{129}{360}$

For Ebford Athletics:

Angle for silver = $144^{\circ}$

Total medals = 70

Proportion of silver medals = $\frac{144}{360}$

Now, we can express these proportions as fractions:

Hamstead Harriers: $\frac{129}{360} \approx 0.3583$

Ebford Athletics: $\frac{144}{360} = \frac{2}{5} = 0.4$

Since $0.4 > 0.3583$, Ebford Athletics won a higher proportion of silver medals.

b) Calculating the Number of Silver Medals for each team:

Number of silver medals = proportion of silver * total medals

Hamstead Harriers:

Number of silver medals = $\frac{129}{360} * 120 = \frac{129}{3} = 43$

Ebford Athletics:

Number of silver medals = $\frac{144}{360} * 70 = \frac{2}{5} * 70 = 2 * 14 = 28$

3. Final Answer

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

b) Hamstead Harriers won 43 silver medals, and Ebford Athletics won 28 silver medals.