The image contains two math problems:

Problem 40:

• Problem Solving: "Before a show, there are 11 groups in a theater. Two groups of 4 people enter, while three groups of 8 people leave. Determine the expression $11 + 2(4) - 3(8)$ and how many people are in the theater."

Problem 41:

• Modeling Real Life: "The tiled door of a house is painted white and blue. Each tile is a square with a side length of 7 inches. What is the area of the door that is painted blue?"

Let's solve these problems step by step.

Problem 40:

We need to calculate the total number of people in the theater after the changes: $11 + 2(4) - 3(8)$

• Start with 11 groups.
• Two groups of 4 people enter: $2 \times 4 = 8$.
• Three groups of 8 people leave: $3 \times 8 = 24$.

Thus, the expression becomes: $11 + 8 - 24 = -5$

Since the result is negative, there might be some issue in terms of physical interpretation, but algebraically, the answer is $-5$.

Problem 41:

The side length of each tile is 7 inches. The area of a square is given by the formula: $\text{Area of square} = \text{side}^2$ So, the area of each tile is: $7^2 = 49 \text{ square inches}.$

If you need the total area of the door painted blue, you will need to know how many tiles are blue.

Would you like more details on either problem, or do you have questions on these solutions?

Related Questions:

1. Can you clarify what "11 groups" refers to in Problem 40?
2. What is the significance of negative numbers in real-life contexts?
3. How would the expression change if only one group entered in Problem 40?
4. How many tiles are blue in Problem 41?
5. How can we calculate the total area of the entire door, including both blue and white tiles?

Tip:

When dealing with word problems, it's essential to ensure all terms in the expression align with the physical context to avoid contradictions like negative people!