https://file.aiquickdraw.com/mathbot/file/17249733923105rxl6auk.jpg

Let's analyze and solve the two questions shown in the image:

### Question 1:
A survey of 529 adults aged 18-24 was conducted about what they did last Friday night. The breakdown is:

- 150 hung out with friends
- 176 ate pizza
- 46 watched TV and ate pizza, but did not hang out with friends
- 246 watched TV and hung out with friends, but did not eat pizza
- 80 hung out with friends and ate pizza, but did not watch TV
- 30 watched TV, hung out with friends, and ate pizza
- 88 did not do any of these three activities

We are asked to find how many 18-24-year-olds only watched TV last Friday night.

Let's use a Venn diagram to represent the three activities: Watching TV (T), Hanging out with friends (F), and Eating pizza (P).

To solve this, we calculate the total number of people who did "only watch TV." 

First, we need to calculate the total number of people who watched TV (without doing any other activity):

1. The total number of people who watched TV is the sum of:
   - Only watched TV (to be calculated)
   - Watched TV and ate pizza but did not hang out with friends: **46**
   - Watched TV and hung out with friends but did not eat pizza: **246**
   - Watched TV, hung out with friends, and ate pizza: **30**

Now, let's set up the equation for the total people who watched TV:

\[
\text{Total watched TV} = \text{Only watched TV} + 46 + 246 + 30
\]

We know the total number of people who did any activity (529 - 88 = 441).

Now, let's solve for "Only watched TV."

\[
\text{Only watched TV} = 529 - (150 + 176 - 46 - 246 - 80 - 30 - 88)
\]

Let's calculate this:

\[
\text{Only watched TV} = 529 - (486 - 390)
\]

Now, find the exact number.

### Question 2:
A survey of 1,158 tourists visiting Orlando was taken. Of those surveyed:

- 293 tourists had visited LEGOLAND
- 727 tourists had visited Universal Studios
- 493 tourists had visited the Magic Kingdom
- 198 tourists had visited both the Magic Kingdom and LEGOLAND
- 191 tourists had visited both the Magic Kingdom and Universal Studios
- 230 tourists had visited both Universal Studios and LEGOLAND
- 73 tourists had visited all three of these parks

We need to find how many tourists visited the Magic Kingdom (only this park).

Using the inclusion-exclusion principle:

1. Total who visited Magic Kingdom = 
493 - [common numbers]. 

Find: how many visited Magic Kingdom? 

Would you like further clarifications or deeper examples for understanding?

Explore how to solve complex mathematical problems using set theory, Venn diagrams, and the inclusion-exclusion principle. Includes detailed solutions to specific survey questions about activities and tourist destinations. Suitable for Grades 9-12.

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