Understanding the Health Club Membership Data

The question provides a table showing the percentage distribution of total members (male and female) and male members across five different health clubs: A, B, C, D, and E. We are also given specific numbers for two health clubs: the total number of members in club C is 1764, and the number of male members in club E is 576.

The task is to find the approximate percentage by which the number of male members in health clubs A and C combined is less than the total number of members (male and female) in health clubs B and C combined.

Calculating Total Members Across All Clubs

We know that the total number of members (male & female) in health club C is 1764, and this represents 14% of the total number of members across all five health clubs. Let the total number of members across all clubs be \(T\).

• According to the table, Club C has 14% of the total members.
• So, \(14\%\) of \(T = 1764\).
• Mathematically, \(0.14 \times T = 1764\).
• To find \(T\), we calculate \(T = \frac{1764}{0.14}\).
• \(T = 12600\).

Thus, the total number of members (both male and female) across all health clubs A to E is 12600.

Calculating Total Male Members Across All Clubs

We are given that the number of male members in health club E is 576. According to the table, this number represents 8% of the total number of male members across all five health clubs. Let the total number of male members across all clubs be \(M\).

• According to the table, Club E has 8% of the total male members.
• So, \(8\%\) of \(M = 576\).
• Mathematically, \(0.08 \times M = 576\).
• To find \(M\), we calculate \(M = \frac{576}{0.08}\).
• \(M = 7200\).

Thus, the total number of male members across all health clubs A to E is 7200.

Finding Total Members (Male & Female) in Health Clubs B and C

Now we need to find the combined total members in health clubs B and C. We use the percentage distribution for total members and the total members across all clubs \(T = 12600\).

• Percentage of total members in Club B = 33%.
• Number of members in Club B = \(33\%\) of \(12600 = 0.33 \times 12600 = 4158\).
• Percentage of total members in Club C = 14%.
• Number of members in Club C = \(14\%\) of \(12600 = 0.14 \times 12600 = 1764\) (This was given in the question and matches our calculation).
• Total members in B and C combined = Number of members in B + Number of members in C
• Total members in B and C combined = \(4158 + 1764 = 5922\).

Finding Total Male Members in Health Clubs A and C

Next, we find the combined number of male members in health clubs A and C. We use the percentage distribution for male members and the total male members across all clubs \(M = 7200\).

• Percentage of male members in Club A = 21%.
• Number of male members in Club A = \(21\%\) of \(7200 = 0.21 \times 7200 = 1512\).
• Percentage of male members in Club C = 19%.
• Number of male members in Club C = \(19\%\) of \(7200 = 0.19 \times 7200 = 1368\).
• Total male members in A and C combined = Male members in A + Male members in C
• Total male members in A and C combined = \(1512 + 1368 = 2880\).

Calculating the Percentage Difference

The question asks for the percentage by which the number of male members in A and C (2880) is less than the total number of members in B and C (5922). The difference is calculated relative to the number of members in B and C.

• Difference = (Total members in B and C) - (Total male members in A and C)
• Difference = \(5922 - 2880 = 3042\).
• Percentage Less = \( \left( \frac{\text{Difference}}{\text{Total members in B and C}} \right) \times 100\% \)
• Percentage Less = \( \left( \frac{3042}{5922} \right) \times 100\% \)
• Percentage Less \( \approx 0.513677 \times 100\% \)
• Percentage Less \( \approx 51.37\%\).

The number of male members in health clubs A and C is approximately 51.37% less than the number of members (both male and female) of health clubs B and C.

Conclusion

Based on the calculations using the provided data and percentages, the number of male members in health clubs A and C combined is approximately 51.37% less than the total number of members (male and female) in health clubs B and C combined.

Revision Table: Key Calculations

Additional Information: Percentage Calculations

When calculating a percentage difference where one value is "less than" another, it's crucial to identify the base value for the percentage calculation. The base value is typically the number you are comparing against, which comes after "less than" or "more than" in the question's phrasing.

• If value A is \(x\) more than value B, the percentage more is \( \frac{A - B}{B} \times 100\% \). The base is B.
• If value A is \(x\) less than value B, the percentage less is \( \frac{B - A}{B} \times 100\% \). The base is B.

In this problem, we compared the number of male members in A and C (2880) to the total members in B and C (5922), asking how much less the former is than the latter. Therefore, 5922 was the base for our percentage calculation.