A rock band is holding a concert and selling tickets. All of the tickets will either be premium seating OR allow backstage access after the event. They wil sell 1,200 premium seating tickets and 500 that will allow backstage access. If 150 of the tickets will both be premium seating and allow backstage access, how many total tickets will they sell?

Answer

To find the total number of tickets sold by the rock band, we can use the principle of inclusion-exclusion. Here’s how we can solve it step by step:

### Step 1: Identify the given values
- Number of premium seating tickets sold (P) = 1200
- Number of backstage access tickets sold (B) = 500
- Number of tickets that are both premium seating and allow backstage access (P ∩ B) = 150

### Step 2: Use the inclusion-exclusion principle
The total number of tickets sold (P ∪ B) can be calculated using the formula:
\[ P \cup B = P + B - (P \cap B) \]

### Step 3: Substitute the values into the formula
Now, we substitute the values we have into the formula:
\[ P \cup B = 1200 + 500 - 150 \]

### Step 4: Perform the calculations
Now we perform the calculations:
\[ P \cup B = 1200 + 500 = 1700 \]
\[ P \cup B = 1700 - 150 = 1550 \]

### Step 5: Conclusion
Therefore, the total number of tickets sold is:
\[ \text{Total tickets sold} = 1550 \]

### Final Answer
The total number of tickets sold is **1550**.

---