The question in the image is asking about the results of a survey conducted in a town with 5000 people. The survey found the following data regarding language knowledge:

• 45% of the people know language A.
• 25% of the people know language B.
• 10% of the people know language C.
• 5% of the people know both languages A and B.
• 4% of the people know both languages B and C.
• 4% of the people know both languages A and C.
• 3% of the people know all three languages A, B, and C.

The question is asking to find the number of people who know only language A.

Step-by-Step Approach:

1. Total Population: 5000 people.

2. Convert Percentages to Numbers:

   • People who know language A: $45\% \times 5000 = 2250$
   • People who know language B: $25\% \times 5000 = 1250$
   • People who know language C: $10\% \times 5000 = 500$
   • People who know A and B: $5\% \times 5000 = 250$
   • People who know B and C: $4\% \times 5000 = 200$
   • People who know A and C: $4\% \times 5000 = 200$
   • People who know all three (A, B, and C): $3\% \times 5000 = 150$

3. Formula for Only Knowing Language A: To find people who know only language A, we need to subtract those who know other combinations involving A from the total who know A.

   Let the number of people who know only A be denoted as: $\text{Only A} = (\text{Total who know A}) - (\text{A and B}) - (\text{A and C}) + (\text{A, B, and C})$

4. Apply the Values:

   • Total who know A: 2250
   • Know A and B: 250
   • Know A and C: 200
   • Know all three: 150 (since these are counted twice in A and B and A and C)

   Substituting the values: $\text{Only A} = 2250 - (250 - 150) - (200 - 150)$ $\text{Only A} = 2250 - 100 - 50$ $\text{Only A} = 2250 - 150 = 2100$

Thus, 2100 people know only language A.

Would you like more details on this solution or to explore related concepts? Here are some follow-up questions:

1. How would the result change if the population increased by 10% but the percentages remained the same?
2. What is the number of people who know only language B?
3. What is the number of people who know exactly two languages (A and B, B and C, A and C)?
4. How would you compute the number of people who know none of the three languages?
5. What mathematical principles underlie the calculation of overlapping sets like this?

Tip: Problems involving sets, intersections, and unions can be solved systematically using Venn diagrams or set formulas.