Understanding the Health Club Member Data

The question asks us to analyze data from a table showing the distribution of total members and male members across five different health clubs (A, B, C, D, E) in 2022. We are given two key pieces of information: the total number of members in health club C is 1764, and the number of male members in health club E is 576. We need to use this information, along with the percentages in the table, to find the number of female members in health club E and the number of male members in health club B, and then calculate the percentage difference.

Let's look at the provided data table:

Calculating Total Members and Total Male Members

We are given that the total number of members in health club C is 1764. From the table, health club C accounts for 14% of the total number of members (both male and female) across all five clubs. We can use this to find the total number of members.

• Let \(T\) be the total number of members in all five clubs.
• Percentage of total members in C = 14%.
• Number of members in C = 1764.
• So, \(14 \% \text{ of } T = 1764\).
• \( \frac{14}{100} \times T = 1764 \)
• \( T = \frac{1764 \times 100}{14} \)
• \( T = 126 \times 100 = 12600 \)

The total number of members in all five health clubs is 12600.

Similarly, we are given that the number of male members in health club E is 576. From the table, health club E accounts for 8% of the total number of male members across all five clubs. We can use this to find the total number of male members.

• Let \(M\) be the total number of male members in all five clubs.
• Percentage of male members in E = 8%.
• Number of male members in E = 576.
• So, \(8 \% \text{ of } M = 576\).
• \( \frac{8}{100} \times M = 576 \)
• \( M = \frac{576 \times 100}{8} \)
• \( M = 72 \times 100 = 7200 \)

The total number of male members in all five health clubs is 7200.

Finding Male Members in Health Club B

The table shows that health club B has 32% of the total male members. We know the total number of male members is 7200.

• Number of male members in B = 32% of Total Male Members
• Number of male members in B = \( \frac{32}{100} \times 7200 \)
• Number of male members in B = \( 32 \times 72 \)
• Number of male members in B = 2304

There are 2304 male members in health club B.

Determining Female Members in Health Club E

First, we need to find the total number of members in health club E. The table shows that health club E has 12% of the total number of members. We know the total number of members is 12600.

• Total members in E = 12% of Total Members
• Total members in E = \( \frac{12}{100} \times 12600 \)
• Total members in E = \( 12 \times 126 \)
• Total members in E = 1512

The total number of members in health club E is 1512. We are given that the number of male members in health club E is 576.

• Number of female members in E = Total members in E - Number of male members in E
• Number of female members in E = \( 1512 - 576 \)
• Number of female members in E = 936

There are 936 female members in health club E.

Calculating the Percentage Difference

We need to find out what percentage the number of female members in health club E (936) is less than the number of male members in health club B (2304). The formula for percentage less than is:

\( \text{Percentage less} = \left( \frac{\text{Value 1 - Value 2}}{\text{Value 2}} \right) \times 100 \% \) if we want to find how much Value 1 is less than Value 2.

Here, Value 1 is female members in E (936) and Value 2 is male members in B (2304).

• Difference = Male members in B - Female members in E
• Difference = \( 2304 - 936 = 1368 \)
• Percentage less = \( \left( \frac{\text{Difference}}{\text{Male members in B}} \right) \times 100 \% \)
• Percentage less = \( \left( \frac{1368}{2304} \right) \times 100 \% \)

Now, we simplify the fraction \( \frac{1368}{2304} \):

• Divide both by 8: \( \frac{1368 \div 8}{2304 \div 8} = \frac{171}{288} \)
• Divide both by 9: \( \frac{171 \div 9}{288 \div 9} = \frac{19}{32} \)

So, the percentage less is \( \left( \frac{19}{32} \right) \times 100 \% = \frac{1900}{32} \% \).

Let's convert the fraction \( \frac{1900}{32} \) to a mixed number:

• \( 1900 \div 32 \)
• \( 1900 = 32 \times 59 + 12 \)
• So, \( \frac{1900}{32} = 59 \frac{12}{32} \)
• Simplify the fraction \( \frac{12}{32} \) by dividing both by 4: \( \frac{12 \div 4}{32 \div 4} = \frac{3}{8} \)

Therefore, the percentage less is \( 59 \frac{3}{8} \% \).

Revision Table: Health Club Member Calculations

Here is a summary of the key calculations performed:

Additional Information: Percentage Concepts

Understanding percentages is crucial for data interpretation questions like this. A percentage is simply a fraction out of 100. For example, 14% means \( \frac{14}{100} \).

To find 'X% of a number Y', you calculate \( \frac{X}{100} \times Y \).

To find what percentage A is of B, you calculate \( \left( \frac{A}{B} \right) \times 100 \% \).

To find what percentage A is less than B, you calculate the difference \( (B - A) \) and then find what percentage this difference is of B. The formula is \( \left( \frac{B - A}{B} \right) \times 100 \% \).

In this problem, we calculated the percentage by which female members in E are less than male members in B using the formula \( \left( \frac{\text{Male Members in B - Female Members in E}}{\text{Male Members in B}} \right) \times 100 \% \).