Analyzing Player Participation Data

The question asks us to find the ratio of male players from Spain to female players from Australia, based on the total number of players participating in Football, Cricket, and Badminton from these countries as provided in the table.

Understanding the Data Table

The table shows the number of players from six different countries participating in three different games: Football, Cricket, and Badminton.

Calculating Total Players per Country

First, we need to find the total number of players from Spain and Australia across all three games.

• Total players from Spain = Players in Football + Players in Cricket + Players in Badminton
• Total players from Spain = 80 + 70 + 95 = 245 players.

• Total players from Australia = Players in Football + Players in Cricket + Players in Badminton
• Total players from Australia = 90 + 85 + 95 = 270 players.

Determining Male Players from Spain

The question states that 60% of the players participating in all games from Spain are male.

• Number of male players from Spain = 60% of Total players from Spain
• Number of male players from Spain = \( \frac{60}{100} \times 245 \)
• Number of male players from Spain = \( 0.60 \times 245 \)
• Number of male players from Spain = 147 players.

Determining Female Players from Australia

The question states that 30% of the players participating in all games from Australia are female.

• Number of female players from Australia = 30% of Total players from Australia
• Number of female players from Australia = \( \frac{30}{100} \times 270 \)
• Number of female players from Australia = \( 0.30 \times 270 \)
• Number of female players from Australia = 81 players.

Calculating the Ratio of Male Spain to Female Australia

We need to find the ratio of male players from Spain to female players from Australia (male : female).

• Ratio = Number of male players from Spain : Number of female players from Australia
• Ratio = 147 : 81

Simplifying the Ratio

To express the ratio in its simplest form, we need to find the greatest common divisor (GCD) of 147 and 81. Both numbers are divisible by 3.

• \( 147 \div 3 = 49 \)
• \( 81 \div 3 = 27 \)
• The simplified ratio is 49 : 27.

This ratio represents the proportion of male players from Spain compared to female players from Australia based on the given percentages and player data.

Revision Table: Key Calculations

Additional Information: Understanding Ratios

A ratio is a comparison of two quantities. It shows how many times one quantity is contained within another. Ratios can be written in various ways, such as \(a:b\), \(a/b\), or "a to b". Simplifying a ratio means dividing both parts of the ratio by their greatest common divisor (GCD) to express it in its lowest terms. This does not change the relationship between the two quantities, just the numbers used to represent it.

Percentages are often used with ratios to represent parts of a whole. Converting a percentage to a decimal (dividing by 100) allows for easy calculation of the value it represents within a total amount.