Calculate Ratio of Players in Two Games

The question asks for the ratio of the total number of players participating in Game A to the total number of players participating in Game B across six different schools. We are given a table showing the number of players from each school in both games.

Analyzing the Player Data Table

Let's look at the data provided in the table:

Calculating Total Players in Each Game

To find the ratio of the total number of players in Game A to the total number of players in Game B, we first need to sum up the players for each game across all schools.

Total players in Game A:

Sum the players from Game A column for schools J, K, L, M, N, and P.

\( \text{Total A} = 31 + 24 + 18 + 29 + 12 + 40 \)

Let's add these numbers:

• \( 31 + 24 = 55 \)
• \( 55 + 18 = 73 \)
• \( 73 + 29 = 102 \)
• \( 102 + 12 = 114 \)
• \( 114 + 40 = 154 \)

So, the total number of players participating in Game A across all schools is \( 154 \).

Total players in Game B:

Sum the players from Game B column for schools J, K, L, M, N, and P.

\( \text{Total B} = 58 + 36 + 26 + 37 + 33 + 44 \)

Let's add these numbers:

• \( 58 + 36 = 94 \)
• \( 94 + 26 = 120 \)
• \( 120 + 37 = 157 \)
• \( 157 + 33 = 190 \)
• \( 190 + 44 = 234 \)

So, the total number of players participating in Game B across all schools is \( 234 \).

Determining the Ratio of Total Players

The question asks for the ratio of the total number of players in Game A to the total number of players in Game B.

Ratio \( = \text{Total A} : \text{Total B} \)

Ratio \( = 154 : 234 \)

Now, we need to simplify this ratio. Both 154 and 234 are even numbers, so they are divisible by 2.

\( 154 \div 2 = 77 \)

\( 234 \div 2 = 117 \)

So, the simplified ratio is \( 77 : 117 \).

Let's check if 77 and 117 have any common factors. 77 is \( 7 \times 11 \). 117 is not divisible by 7 or 11. It is divisible by 3 (\( 1+1+7=9 \), which is divisible by 3). \( 117 \div 3 = 39 \). So, \( 117 = 3 \times 39 = 3 \times 3 \times 13 \). Since 77 and 117 have no common factors other than 1, the ratio \( 77 : 117 \) is in its simplest form.

Conclusion: The Final Ratio

The ratio of the total number of players participating in Game A to the total number of players participating in Game B is \( 77 : 117 \).

Revision Table: Game Player Analysis Summary

Here is a summary of the total players in each game:

Additional Information: Understanding Ratios

A ratio is a way to compare two quantities. It shows how many times one quantity is contained in another or how the two quantities relate to each other. Ratios can be written with a colon (e.g., A:B), as a fraction (\( \frac{A}{B} \)), or with the word "to" (A to B).

To simplify a ratio, you divide both parts of the ratio by their greatest common divisor (GCD). This is similar to simplifying a fraction. In this case, the GCD of 154 and 234 is 2.

Ratios are dimensionless quantities, meaning they do not have units. They are widely used in various fields, including mathematics, science, and everyday life, to express relationships between numbers.