### Birthday Party Budget Planning Exercise**Scenario:**Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50 each, and a small bag of popcorn costs $4.50.**Task:**Emilio writes the inequality $ 17(f + 2) + 45.99 \leq 200 $ to better represent the situation, using the variable $ f $ to represent the number of friends. Solve the inequality. Round your answer to the nearest hundredth. Then write the maximum number of friends that can attend the birthday party. Enter your answers in the boxes.\[f \leq \_\_\_\_\_\_\_\]Tomas and Emilio can invite \_\_\_\_\_\_\_ friends.### Steps to Solve the Problem:1. **Understand the Inequality:** \[ 17(f + 2) + 45.99 \leq 200 \] - **17:** Represents the combined cost of 1 movie ticket ($12.50) and 1 small bag of popcorn ($4.50). - **(f + 2):** Represents the number of people, including Tomas and Emilio, attending the party. 2. **Distribute and Combine Like Terms:** \[ 17f + 34 + 45.99 \leq 200 \]3. **Simplify the Expression:** \[ 17f + 79.99 \leq 200 \]4. **Isolate the Variable $ f $:** \[ 17f \leq 120.01 \] \[ f \leq \frac{120.01}{17} \] \[ f \leq 7.06 \]5. **Interpret the Result:** - Tomas and Emilio can invite up to 7 friends, rounding down since inviting a fraction of a friend is not possible.### Final Answers:\[f \leq 7.06 \]Tomas and Emilio can invite $\boxed{7}$ friends.This exercise involves understanding and solving inequalities, which is a crucial skill in algebra and practical budget planning.

Answered: Image /qna-images/answer/62893981-1fc9-42cc-b363-13c2bbcbf521.jpg

Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50 each, and a small bag of popcorn costs $4.50. Emilio writes the inequality 17(f + 2) + 45.99 < 200 to better represent the situation, using the variable f to represent the number of friends. Solve the inequality. Round your answer to the nearest hundredth. Then write the maximum number of friends that can attend the birthday party. Enter your answers in the boxes. fs Tomas and Emilio can invite friends.

Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50 each, and a small bag of popcorn costs $4.50. Emilio writes the inequality 17(f + 2) + 45.99 < 200 to better represent the situation, using the variable f to represent the number of friends. Solve the inequality. Round your answer to the nearest hundredth. Then write the maximum number of friends that can attend the birthday party. Enter your answers in the boxes. fs Tomas and Emilio can invite friends.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Birthday Party Budget Planning Exercise

**Scenario:**

Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50 each, and a small bag of popcorn costs $4.50.

**Task:**

Emilio writes the inequality $ 17(f + 2) + 45.99 \leq 200 $ to better represent the situation, using the variable $ f $ to represent the number of friends. Solve the inequality. Round your answer to the nearest hundredth. Then write the maximum number of friends that can attend the birthday party. Enter your answers in the boxes.

\[
f \leq \_\_\_\_\_\_\_
\]

Tomas and Emilio can invite \_\_\_\_\_\_\_ friends.

### Steps to Solve the Problem:

1. **Understand the Inequality:**
\[
17(f + 2) + 45.99 \leq 200
\]

- **17:** Represents the combined cost of 1 movie ticket ($12.50) and 1 small bag of popcorn ($4.50).
- **(f + 2):** Represents the number of people, including Tomas and Emilio, attending the party.

2. **Distribute and Combine Like Terms:**
\[
17f + 34 + 45.99 \leq 200
\]

3. **Simplify the Expression:**
\[
17f + 79.99 \leq 200
\]

4. **Isolate the Variable $ f $:**
\[
17f \leq 120.01
\]
\[
f \leq \frac{120.01}{17}
\]
\[
f \leq 7.06
\]

5. **Interpret the Result:**
- Tomas and Emilio can invite up to 7 friends, rounding down since inviting a fraction of a friend is not possible.

### Final Answers:

\[
f \leq 7.06
\]

Tomas and Emilio can invite $\boxed{7}$ friends.

This exercise involves understanding and solving inequalities, which is a crucial skill in algebra and practical budget planning.

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