3. John and six of his friends are going to a LI Ducks baseball game. Their combined money totals $35.25. At the game each hamburger costs $7.50 and each popcorn bucket costs $2.50, and soda costs $0.75 each. Each person buys one soda. They spend all $35.25 on foyd and soda. Write an equation that can determine the number of popcorn buckets, x and hamburgers, y, John and his friends can buy. Graph your equation on the grid below.
3. John and six of his friends are going to a LI Ducks baseball game. Their combined money totals $35.25. At the game each hamburger costs $7.50 and each popcorn bucket costs $2.50, and soda costs $0.75 each. Each person buys one soda. They spend all $35.25 on foyd and soda. Write an equation that can determine the number of popcorn buckets, x and hamburgers, y, John and his friends can buy. Graph your equation on the grid below.
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
![### Problem Statement:
**John and six of his friends are going to a LI Ducks baseball game. Their combined money totals $35.25. At the game each hamburger costs $7.50 and each bucket of popcorn costs $2.50, and soda costs $0.75 each. Each person buys one soda. They spend all $35.25 on food and soda.**
**Write an equation that can determine the number of popcorn buckets, \( x \), and hamburgers, \( y \), John and his friends can buy.**
Graph your equation on the grid below.
### Solution Steps:
1. **Understand the given information:**
- Total money: $35.25
- Cost of one hamburger: $7.50
- Cost of one popcorn bucket: $2.50
- Cost of one soda: $0.75
- Each of the seven people (John and six friends) buys one soda, so:
\( 7 \times 0.75 = 5.25 \)
- Remaining money for hamburgers and popcorn after buying sodas:
\( 35.25 - 5.25 = 30.00 \)
2. **Translate the problem into an equation:**
Let \( x \) represent the number of popcorn buckets and \( y \) represent the number of hamburgers. The equation representing the total expenditure on food (excluding soda) is:
\[
2.50x + 7.50y = 30.00
\]
3. **Graph the equation on the provided grid:**
The graph would represent the possible combinations of \( x \) (popcorn buckets) and \( y \) (hamburgers) that total $30.00.
#### Steps to graph:
- Put \( x \) (number of popcorn buckets) on the x-axis.
- Put \( y \) (number of hamburgers) on the y-axis.
- Find the intercepts:
- \(x\)-intercept: Set \( y = 0 \).
\[
2.50x = 30.00 \implies x = 12
\]
- \(y\)-intercept: Set \( x = 0 \).
\[
7.50y = 30.00 \implies y = 4
\]
- Plot the points:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4eae88c4-db1c-43d3-90e9-8943432b1468%2Fdd5ae433-180b-48e3-94d4-cf92c290252d%2Fmglaon8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
**John and six of his friends are going to a LI Ducks baseball game. Their combined money totals $35.25. At the game each hamburger costs $7.50 and each bucket of popcorn costs $2.50, and soda costs $0.75 each. Each person buys one soda. They spend all $35.25 on food and soda.**
**Write an equation that can determine the number of popcorn buckets, \( x \), and hamburgers, \( y \), John and his friends can buy.**
Graph your equation on the grid below.
### Solution Steps:
1. **Understand the given information:**
- Total money: $35.25
- Cost of one hamburger: $7.50
- Cost of one popcorn bucket: $2.50
- Cost of one soda: $0.75
- Each of the seven people (John and six friends) buys one soda, so:
\( 7 \times 0.75 = 5.25 \)
- Remaining money for hamburgers and popcorn after buying sodas:
\( 35.25 - 5.25 = 30.00 \)
2. **Translate the problem into an equation:**
Let \( x \) represent the number of popcorn buckets and \( y \) represent the number of hamburgers. The equation representing the total expenditure on food (excluding soda) is:
\[
2.50x + 7.50y = 30.00
\]
3. **Graph the equation on the provided grid:**
The graph would represent the possible combinations of \( x \) (popcorn buckets) and \( y \) (hamburgers) that total $30.00.
#### Steps to graph:
- Put \( x \) (number of popcorn buckets) on the x-axis.
- Put \( y \) (number of hamburgers) on the y-axis.
- Find the intercepts:
- \(x\)-intercept: Set \( y = 0 \).
\[
2.50x = 30.00 \implies x = 12
\]
- \(y\)-intercept: Set \( x = 0 \).
\[
7.50y = 30.00 \implies y = 4
\]
- Plot the points:
![**Title: Analyzing Budget Combinations: Popcorn Buckets and Hamburgers**
**Introduction**
This exercise aims to explore the different combinations of items that can be purchased with a fixed budget. Our focus is to determine the various combinations of popcorn buckets and hamburgers that John and his friends can buy with a total amount of $35.25. This involves understanding and applying basic concepts of arithmetic and possibly algebra to list all possible item combinations within the given budget constraint.
---
**Problem Statement**
"Determine how many different combinations, including those combinations containing zero, of popcorn buckets and hamburgers John and his friends can buy, spending all $35.25."
---
**Detailed Explanation**
We'll approach this problem by breaking it down into steps:
1. **Identify Prices:** First, ascertain the prices of both items, popcorn buckets and hamburgers. For example, if a popcorn bucket costs $5.00 and a hamburger costs $4.50, you need to find all combinations of these two items that total $35.25.
2. **Set Up Equations:** Formulate an equation representing the total spend:
\[
5.00x + 4.50y = 35.25
\]
Where \( x \) is the number of popcorn buckets and \( y \) is the number of hamburgers.
3. **Solve for Combinations:** Solve the equation for all possible non-negative integer values of \( x \) and \( y \) that satisfy spending exactly $35.25.
4. **Consider Zero Combinations:** Include combinations where either \( x \) or \( y \) can be zero.
5. **Graphical Representation (If Applicable):** Utilize a graph to visually represent the solution set. Each point on the graph where the total cost equals $35.25 represents a valid purchase combination.
**Note:** This explanation assumes arbitrary prices for popcorn buckets and hamburgers as they were not provided in the problem statement.
---
**Conclusion**
By following the steps outlined above, one can determine all possible combinations of popcorn buckets and hamburgers that total the given budget. This kind of practical problem-solving helps to reinforce basic arithmetic skills and introduces elementary algebraic concepts to students in an engaging way.
---
**Additional Resources**
- **Interactive Budget Calculator:** Use our online tool to input different prices and budget amounts to dynamically see possible item combinations.
- **Algebra Tutorials:** Visit our algebra section for more detailed lessons on setting up](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4eae88c4-db1c-43d3-90e9-8943432b1468%2Fdd5ae433-180b-48e3-94d4-cf92c290252d%2Fq4wahgp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing Budget Combinations: Popcorn Buckets and Hamburgers**
**Introduction**
This exercise aims to explore the different combinations of items that can be purchased with a fixed budget. Our focus is to determine the various combinations of popcorn buckets and hamburgers that John and his friends can buy with a total amount of $35.25. This involves understanding and applying basic concepts of arithmetic and possibly algebra to list all possible item combinations within the given budget constraint.
---
**Problem Statement**
"Determine how many different combinations, including those combinations containing zero, of popcorn buckets and hamburgers John and his friends can buy, spending all $35.25."
---
**Detailed Explanation**
We'll approach this problem by breaking it down into steps:
1. **Identify Prices:** First, ascertain the prices of both items, popcorn buckets and hamburgers. For example, if a popcorn bucket costs $5.00 and a hamburger costs $4.50, you need to find all combinations of these two items that total $35.25.
2. **Set Up Equations:** Formulate an equation representing the total spend:
\[
5.00x + 4.50y = 35.25
\]
Where \( x \) is the number of popcorn buckets and \( y \) is the number of hamburgers.
3. **Solve for Combinations:** Solve the equation for all possible non-negative integer values of \( x \) and \( y \) that satisfy spending exactly $35.25.
4. **Consider Zero Combinations:** Include combinations where either \( x \) or \( y \) can be zero.
5. **Graphical Representation (If Applicable):** Utilize a graph to visually represent the solution set. Each point on the graph where the total cost equals $35.25 represents a valid purchase combination.
**Note:** This explanation assumes arbitrary prices for popcorn buckets and hamburgers as they were not provided in the problem statement.
---
**Conclusion**
By following the steps outlined above, one can determine all possible combinations of popcorn buckets and hamburgers that total the given budget. This kind of practical problem-solving helps to reinforce basic arithmetic skills and introduces elementary algebraic concepts to students in an engaging way.
---
**Additional Resources**
- **Interactive Budget Calculator:** Use our online tool to input different prices and budget amounts to dynamically see possible item combinations.
- **Algebra Tutorials:** Visit our algebra section for more detailed lessons on setting up
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