Of 320 consumers polled, some purchase Blu-ray movies, some only purchase movies on DVD, and some do both. If 300 people polled purchase Blu-ray discs and 280 purchase DVDs and Blu-ray discs, how many people only buy DVDs?

Since B+D-(B&D) = 320,

300 + D - 280 = 320
D = 300

300-280 = 20 buy only DVDs.

Or, you can reason that if 300 bought Blu-ray, and 280 of those also bought DVD, then only 20 bought just Blu-ray.

So, That means that the remaining 20 bought only DVDs

To find out how many people only buy DVDs, we need to determine the number of people who purchase both DVDs and Blu-ray discs and subtract that number from the total number of people who purchase DVDs.

Let's go step-by-step:

Step 1: Start with the total number of people who purchase DVDs and Blu-ray discs, which is 280.

Step 2: Subtract the number of people who purchase both DVDs and Blu-ray discs from this total. According to the information given, the total number of people who purchase only Blu-ray discs is 300.

280 - 300 = -20

Step 3: Interpret the result. Since we cannot have a negative number of people, the result of -20 indicates an error or inconsistent data in the information provided. Please review the data and correct any inconsistencies to proceed with a valid calculation.

To find the number of people who only buy DVDs, we need to subtract the number of people who buy both Blu-ray discs and DVDs from the total number of people who buy DVDs.

Given:

Total number of consumers polled (N) = 320
Number of people who purchase Blu-ray discs (B) = 300
Number of people who purchase DVDs and Blu-ray discs (B&D) = 280

To find the number of people who only buy DVDs:

Step 1: Calculate the number of people who buy both Blu-ray discs and DVDs (B&D).

B&D = Number of Blu-ray discs (B) + Number of DVDs (D) - Total consumers polled (N)
280 = 300 + D - 320

Step 2: Rearrange the equation to solve for the number of DVDs (D).

D = 280 + 320 - 300
D = 320

Therefore, the number of people who only buy DVDs is 320.