We appreciate your visit to Will brought a 144 ounce cooler filled with water to soccer practice He used 16 ounces from the cooler to fill his water bottle He. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
- Calculate the remaining water after Will fills his bottle: $144 - 16 = 128$ ounces.
- Set up the inequality representing the water distribution: $16x \le 128$.
- Solve for $x$: $x \le 8$.
- Combine with the condition that $x > 0$ to get the final range: $0 < x \le 8$, so the answer is $\boxed{(0, 8]}$.
### Explanation
1. Initial Analysis
Let's analyze the problem. Will starts with a 144-ounce cooler of water. He uses 16 ounces for his own water bottle, leaving $144 - 16 = 128$ ounces. He then distributes the remaining water into 16 cups, with each cup receiving $x$ ounces. We need to find the possible values of $x$.
2. Setting up the Inequality
The total amount of water distributed into the 16 cups is $16x$ ounces. This amount must be less than or equal to the remaining water in the cooler, which is 128 ounces. This gives us the inequality $16x \le 128$.
3. Solving for x
To solve for $x$, we divide both sides of the inequality by 16:$$\frac{16x}{16} \le \frac{128}{16}$$$$x \le 8$$
4. Determining the Range of x
Since Will is putting water into the cups, the amount of water in each cup must be greater than 0. So, $x > 0$. Combining this with the previous inequality, we get $0 < x \le 8$. This means that each cup can contain any amount of water greater than 0 ounces and up to 8 ounces, inclusive.
5. Final Answer and Graphing
Therefore, the number of ounces of water, $x$, that Will could have put in each cup is greater than 0 and less than or equal to 8. In interval notation, this is $(0, 8]$. To graph this on a number line, we would draw a line segment from 0 to 8. There would be an open circle at 0 (since $x$ cannot be equal to 0) and a closed circle at 8 (since $x$ can be equal to 8).
### Examples
Understanding inequalities like this can help in various real-life scenarios. For instance, if you're distributing snacks among a group of friends, and you have a limited amount of each snack, you can use inequalities to determine the possible amounts each person can receive while ensuring everyone gets something and you don't exceed your supply. This applies to resource allocation, budgeting, and even planning events where you need to manage quantities effectively.
- Set up the inequality representing the water distribution: $16x \le 128$.
- Solve for $x$: $x \le 8$.
- Combine with the condition that $x > 0$ to get the final range: $0 < x \le 8$, so the answer is $\boxed{(0, 8]}$.
### Explanation
1. Initial Analysis
Let's analyze the problem. Will starts with a 144-ounce cooler of water. He uses 16 ounces for his own water bottle, leaving $144 - 16 = 128$ ounces. He then distributes the remaining water into 16 cups, with each cup receiving $x$ ounces. We need to find the possible values of $x$.
2. Setting up the Inequality
The total amount of water distributed into the 16 cups is $16x$ ounces. This amount must be less than or equal to the remaining water in the cooler, which is 128 ounces. This gives us the inequality $16x \le 128$.
3. Solving for x
To solve for $x$, we divide both sides of the inequality by 16:$$\frac{16x}{16} \le \frac{128}{16}$$$$x \le 8$$
4. Determining the Range of x
Since Will is putting water into the cups, the amount of water in each cup must be greater than 0. So, $x > 0$. Combining this with the previous inequality, we get $0 < x \le 8$. This means that each cup can contain any amount of water greater than 0 ounces and up to 8 ounces, inclusive.
5. Final Answer and Graphing
Therefore, the number of ounces of water, $x$, that Will could have put in each cup is greater than 0 and less than or equal to 8. In interval notation, this is $(0, 8]$. To graph this on a number line, we would draw a line segment from 0 to 8. There would be an open circle at 0 (since $x$ cannot be equal to 0) and a closed circle at 8 (since $x$ can be equal to 8).
### Examples
Understanding inequalities like this can help in various real-life scenarios. For instance, if you're distributing snacks among a group of friends, and you have a limited amount of each snack, you can use inequalities to determine the possible amounts each person can receive while ensuring everyone gets something and you don't exceed your supply. This applies to resource allocation, budgeting, and even planning events where you need to manage quantities effectively.
Thanks for taking the time to read Will brought a 144 ounce cooler filled with water to soccer practice He used 16 ounces from the cooler to fill his water bottle He. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
