A Sponsor Donates $\$5$ For Every $\frac{1}{3}$ Mile That Each Of The Following Participants Runs In A Fundraiser. How Much Money Does The Sponsor Donate In Total?\[\begin{tabular}{|c|c|}\hline \multicolumn{2}{|c|}{\textbf{Donation

Introduction

In a recent fundraiser, a generous sponsor has agreed to donate a significant amount of money to support the participants. The sponsor has pledged to donate $\$5$ for every $\frac{1}{3}$ mile that each participant runs. In this article, we will explore the total amount of money that the sponsor will donate based on the information provided.

Understanding the Donation Rate

To calculate the total amount of money donated by the sponsor, we need to understand the donation rate. The sponsor donates $\$5$ for every $\frac{1}{3}$ mile that each participant runs. This means that for every $\frac{1}{3}$ mile, the sponsor will donate $\$5$. To find the total amount of money donated, we need to multiply the donation rate by the total number of $\frac{1}{3}$ miles run by all participants.

Calculating the Total Number of $\frac{1}{3}$ Miles

Let's assume that there are $n$ participants in the fundraiser. Each participant runs a certain distance, and we need to find the total number of $\frac{1}{3}$ miles run by all participants. If we let $d_i$ be the distance run by participant $i$, then the total number of $\frac{1}{3}$ miles run by all participants is given by:

$$\sum_{i=1}^n \left\lfloor \frac{d_i}{\frac{1}{3}} \right\rfloor$$

where $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$.

Calculating the Total Amount of Money Donated

Now that we have the total number of $\frac{1}{3}$ miles run by all participants, we can calculate the total amount of money donated by the sponsor. The sponsor donates $\$5$ for every $\frac{1}{3}$ mile, so the total amount of money donated is given by:

$$\sum_{i=1}^n \left\lfloor \frac{d_i}{\frac{1}{3}} \right\rfloor \times 5$$

Example Calculations

Let's consider an example to illustrate the calculation. Suppose there are 5 participants in the fundraiser, and each participant runs the following distances:

To calculate the total amount of money donated, we need to find the total number of $\frac{1}{3}$ miles run by all participants. We can do this by dividing each participant's distance by $\frac{1}{3}$ and rounding down to the nearest integer:

The total number of $\frac{1}{3}$ miles run by all participants is:

$$6 + 10 + 5 + 7 + 12 = 40$$

Now, we can calculate the total amount of money donated by multiplying the total number of $\frac{1}{3}$ miles by $\$5$:

$$40 \times 5 = 200$$

Therefore, the sponsor will donate a total of $\$200$ to support the participants in the fundraiser.

Conclusion

Introduction

In our previous article, we explored the total amount of money donated by a sponsor in a fundraiser. The sponsor donates $\$5$ for every $\frac{1}{3}$ mile that each participant runs. In this article, we will answer some frequently asked questions related to the sponsor's donation.

Q&A

Q: How does the sponsor's donation rate work?

A: The sponsor donates $\$5$ for every $\frac{1}{3}$ mile that each participant runs. This means that for every $\frac{1}{3}$ mile, the sponsor will donate $\$5$.

Q: What if a participant runs a distance that is not a multiple of $\frac{1}{3}$ miles?

A: In this case, the participant's distance will be rounded down to the nearest multiple of $\frac{1}{3}$ miles. For example, if a participant runs 2.1 miles, their distance will be rounded down to 2 miles, which is equivalent to 6 $\frac{1}{3}$ miles.

Q: How do I calculate the total amount of money donated by the sponsor?

A: To calculate the total amount of money donated, you need to find the total number of $\frac{1}{3}$ miles run by all participants. You can do this by dividing each participant's distance by $\frac{1}{3}$ and rounding down to the nearest integer. Then, you multiply the total number of $\frac{1}{3}$ miles by $\$5$.

Q: What if there are multiple participants in the fundraiser?

A: If there are multiple participants in the fundraiser, you need to find the total number of $\frac{1}{3}$ miles run by all participants. You can do this by summing up the number of $\frac{1}{3}$ miles run by each participant.

Q: Can I use a calculator to calculate the total amount of money donated?

A: Yes, you can use a calculator to calculate the total amount of money donated. Simply enter the total number of $\frac{1}{3}$ miles run by all participants and multiply it by $\$5$.

Q: What if the sponsor's donation rate changes?

A: If the sponsor's donation rate changes, you will need to recalculate the total amount of money donated based on the new donation rate.

Q: Can I use this method to calculate the total amount of money donated for other types of fundraisers?

A: Yes, you can use this method to calculate the total amount of money donated for other types of fundraisers, as long as the donation rate is based on a fixed distance.

Conclusion

In this article, we have answered some frequently asked questions related to the sponsor's donation. We hope that this Q&A article has provided you with a better understanding of how to calculate the total amount of money donated by the sponsor. If you have any further questions, please don't hesitate to ask.

Additional Resources

• Previous article: A Sponsor's Generous Donation: Calculating the Total Amount
• Calculator tool: Total Amount of Money Donated

Disclaimer

The information provided in this article is for educational purposes only. It is not intended to be used as a substitute for professional advice. If you have any questions or concerns, please consult with a qualified professional.