Use the pie chart to complete the table. The Under 13's played 28 matches. The Under 15's played 18 matches. Which team won more matches? Show your workings.

Steps to Solve

1. Calculate Total Number of Fans The total degrees in a pie chart is $360^{\circ}$.

The angles given are:

• England: $120^{\circ}$
• Scotland: $45^{\circ}$
• Wales: $45^{\circ}$
• France: $45^{\circ}$
• Ireland: $90^{\circ}$

Add these angles together: $$120 + 45 + 45 + 45 + 90 = 345^{\circ}$$

The remaining angle for the total degrees must account for the number of fans.

2. Determine Proportions of Total Fans With the total angle of $360^{\circ}$, we need to find the total number of fans who supported the rugby teams:

Let ( x ) = total number of fans.

Using the formula for proportions: $$\frac{120}{360} = \frac{\text{Number of fans supporting England}}{x}$$

From this proportion, calculate the number of fans supporting England: $$ \text{Number of fans supporting England} = x \cdot \frac{120}{360} = \frac{1}{3}x $$

3. Set Up Equations for Other Teams Using similar equations for the other teams:

• For Scotland: $$ \text{Number of fans supporting Scotland} = x \cdot \frac{45}{360} = \frac{1}{8}x $$

• For Wales: $$ \text{Number of fans supporting Wales} = x \cdot \frac{45}{360} = \frac{1}{8}x $$

• For France: $$ \text{Number of fans supporting France} = x \cdot \frac{45}{360} = \frac{1}{8}x $$

• For Ireland: $$ \text{Number of fans supporting Ireland} = x \cdot \frac{90}{360} = \frac{1}{4}x $$

4. Total Fans Calculation Now, we can sum these up: $$ \frac{1}{3}x + \frac{1}{8}x + \frac{1}{8}x + \frac{1}{8}x + \frac{1}{4}x = x $$

Finding a common denominator (24): $$ \frac{8}{24}x + \frac{3}{24}x + \frac{3}{24}x + \frac{3}{24}x + \frac{6}{24}x = 1x $$

Combine fractions: $$ \frac{23}{24}x = x $$

5. Calculate Number of Fans for Each Team Now we can setup from known ( x ) values. Assuming a total of $N$ fans:

• For England: $N * \frac{120}{360} = N * \frac{1}{3}$
• For Scotland: $N * \frac{45}{360} = N * \frac{1}{8}$
• For Wales: $N * \frac{45}{360} = N * \frac{1}{8}$
• For France: $N * \frac{45}{360} = N * \frac{1}{8}$
• For Ireland: $N * \frac{90}{360} = N * \frac{1}{4}$ You can check with known fan counts, then fill accordingly.

6. Under 13's and Under 15's Matches The Under 13's played 28 matches, to calculate wins based on the pie chart.

• Total matches played by Under 15's = 18.
• Angle for matches won = $120^{\circ}$.

Using proportions, determine: $$ \text{for Under 15} = \frac{120}{360} \times 18 = 6 \text{ won}$$

7. Determine Winning Team To compare teams, identify wins:

• For Under 13's, subtract: $$ \text{Lost} = 28 - \text{Won}$$

Now compare teams to find who won more matches.