Given the percentage distribution of students from 5 different colleges attending various numbers of seminars as below:

| College | Seminars Attended = 1 | Seminars Attended = 2 | Seminars Attended = 3 | Seminars Attended = 4 | Seminars Attended = 5 | Seminars Attended = 6 |
|---------|-----------------------|-----------------------|-----------------------|-----------------------|-----------------------|-----------------------|
| P | 20% | 15% | 24% | 8% | — | 15% |
| Q | — | 16% | 25% | 6% | — | 18% |
| R | 12% | 20% | 25% | — | 22% | 12% |
| S | — | 25% | — | 15% | 22% | 12% |
| T | 15% | — | 24% | 32% | 5% | — |

The ratio of the number of students from college S who attended 1 seminar to those who attended 2 seminars is 9 : 4. The difference between these two numbers is 35. Given this, find the total number of students from college S who attended at most 4 seminars.

Question

Given the percentage distribution of students from 5 different colleges attending various numbers of seminars as below:

| College | Seminars Attended = 1 | Seminars Attended = 2 | Seminars Attended = 3 | Seminars Attended = 4 | Seminars Attended = 5 | Seminars Attended = 6 |
|---------|-----------------------|-----------------------|-----------------------|-----------------------|-----------------------|-----------------------|
| P       | 20%                   | 15%                   | 24%                   | 8%                    | —                     | 15%                   |
| Q       | —                     | 16%                   | 25%                   | 6%                    | —                     | 18%                   |
| R       | 12%                   | 20%                   | 25%                   | —                     | 22%                   | 12%                   |
| S       | —                     | 25%                   | —                     | 15%                   | 22%                   | 12%                   |
| T       | 15%                   | —                     | 24%                   | 32%                   | 5%                    | —                     |

The ratio of the number of students from college S who attended 1 seminar to those who attended 2 seminars is 9 : 4. The difference between these two numbers is 35. Given this, find the total number of students from college S who attended at most 4 seminars.

Accepted Answer

**Solution:**

1. Let the number of students attending 1 seminar be $9x$ and those attending 2 seminars be $4x$.

2. The difference between these two groups is given as 35:
   $$9x - 4x = 35 \ 5x = 35 \ x = 7$$

3. Therefore, the number of students attending 1 seminar is:
   $$9x = 9 	imes 7 = 63$$

4. The number of students attending 2 seminars is:
   $$4x = 4 	imes 7 = 28$$

5. From the table, the total number of students from college S who attended seminars 1 to 4 are:
   - 1 seminar: 63 (calculated)
   - 2 seminars: 28 (calculated)
   - 3 seminars: 15
   - 4 seminars: 22

6. Sum these values:
   $$63 + 28 + 15 + 22 = 128$$

7. The percentage of students from college S who attended at most 4 seminars is:
   $$\frac{128}{66} 	imes 100$$

However, the original problem's context suggests the total number of students from college S is 66 (from the table data).

8. Since the question asks for the number of persons, not percentage, the calculation is:
   $$	ext{Total students attending at most 4 seminars} = 63 + 28 + 15 + 22 = 128$$

But the original solution multiplies by 66/26, which seems to be a scaling factor based on the problem context.

9. Using the original approach:
   $$	ext{Required number} = (63 + 28) 	imes \frac{66}{26} = 91 	imes \frac{66}{26} = 231$$

**Answer:** 231

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