In a certain city of 15000 families, 3.5% of families who read A but not B look into advertisements, 25% of the families who read B but not A look into advertisements and 50% of the families, who read both A and B look into advertisements. It is known that 8000 families read A, 4000 read B and 1000 read both A and B. Find the number of families who look into advertisements

Answer

To solve the problem step by step, we will break down the information given and calculate the number of families who look into advertisements based on their reading habits.

### Step 1: Identify the families reading A and B
- Total families = 15,000
- Families reading A = 8,000
- Families reading B = 4,000
- Families reading both A and B = 1,000

### Step 2: Calculate the families reading only A and only B
- Families reading only A = Families reading A - Families reading both A and B
\[ \text{Families reading only A} = 8000 - 1000 = 7000 \]

- Families reading only B = Families reading B - Families reading both A and B
\[ \text{Families reading only B} = 4000 - 1000 = 3000 \]

### Step 3: Calculate the families looking into advertisements
1. **Families who read A but not B (7000 families)**:
- Percentage looking into advertisements = 3.5%
- Number of families looking into advertisements from this group:
\[ \text{Families looking into ads from A only} = 3.5\% \text{ of } 7000 = \frac{3.5}{100} \times 7000 = 245 \]

2. **Families who read B but not A (3000 families)**:
- Percentage looking into advertisements = 25%
- Number of families looking into advertisements from this group:
\[ \text{Families looking into ads from B only} = 25\% \text{ of } 3000 = \frac{25}{100} \times 3000 = 750 \]

3. **Families who read both A and B (1000 families)**:
- Percentage looking into advertisements = 50%
- Number of families looking into advertisements from this group:
\[ \text{Families looking into ads from both A and B} = 50\% \text{ of } 1000 = \frac{50}{100} \times 1000 = 500 \]

### Step 4: Total families looking into advertisements
Now, we sum up the families looking into advertisements from all groups:
\[ \text{Total families looking into ads} = 245 + 750 + 500 = 1495 \]

### Final Answer
The number of families who look into advertisements is **1495**.

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