Question
This is for math. Real-world problems that involve two quantities that are related, but not necessarily equal, can usually be solved with an inequality. Make up an inequality and solve. What would it look like to communicate your solution clearly if your inequality represented a real-world problem. Then ask your peers if they can come up with a real-world problem that could be solved using your inequality.
Answers
GPT-4o mini
### Problem Description
Let’s say you are planning a fundraising event for a local charity. You need to ensure that the total amount of money raised is greater than a specific target in order to meet your goal. Your goal is to raise at least $500. Additionally, you need to consider that each ticket sold for your fundraising event costs $20.
To represent this situation with an inequality, we can let \( x \) be the number of tickets sold. The inequality to express the condition that the total money raised must be at least $500 can be formulated as:
\[
20x > 500
\]
### Solving the Inequality
To solve for \( x \):
1. Divide both sides of the inequality by 20:
\[
x > \frac{500}{20}
\]
2. Simplify the right side:
\[
x > 25
\]
This means you need to sell more than 25 tickets in order to meet your fundraising goal.
### Communicating the Solution Clearly
To communicate the solution clearly, you could say:
"In order to reach our fundraising goal of at least $500, we need to sell more than 25 tickets to the event. This means that selling 26 tickets or more will allow us to successfully meet our target. Therefore, our focus should be on promoting and selling at least 26 tickets for the event to ensure we achieve our goal."
### Call to Action for Peers
Now, I’d like to ask my peers:
Can you come up with a real-world problem that could be solved using the inequality \( 20x > 500 \)? What scenario might resemble this situation, and how would you set it up?
Let’s say you are planning a fundraising event for a local charity. You need to ensure that the total amount of money raised is greater than a specific target in order to meet your goal. Your goal is to raise at least $500. Additionally, you need to consider that each ticket sold for your fundraising event costs $20.
To represent this situation with an inequality, we can let \( x \) be the number of tickets sold. The inequality to express the condition that the total money raised must be at least $500 can be formulated as:
\[
20x > 500
\]
### Solving the Inequality
To solve for \( x \):
1. Divide both sides of the inequality by 20:
\[
x > \frac{500}{20}
\]
2. Simplify the right side:
\[
x > 25
\]
This means you need to sell more than 25 tickets in order to meet your fundraising goal.
### Communicating the Solution Clearly
To communicate the solution clearly, you could say:
"In order to reach our fundraising goal of at least $500, we need to sell more than 25 tickets to the event. This means that selling 26 tickets or more will allow us to successfully meet our target. Therefore, our focus should be on promoting and selling at least 26 tickets for the event to ensure we achieve our goal."
### Call to Action for Peers
Now, I’d like to ask my peers:
Can you come up with a real-world problem that could be solved using the inequality \( 20x > 500 \)? What scenario might resemble this situation, and how would you set it up?