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?(a) $\$105$ (b) $\$90$ (c) $\$75$ (d)

In a heartwarming display of generosity, a sponsor has pledged to donate $\$5$ for every $\frac{1}{3}$ mile that each participant runs in a fundraiser. The question on everyone's mind is: how much money will the sponsor donate in total? To determine this, we need to calculate the total distance covered by all the participants and then multiply it by the donation amount per $\frac{1}{3}$ mile.

Understanding the Donation Structure

The sponsor's donation structure is straightforward: $\$5$ for every $\frac{1}{3}$ mile. This means that for every $\frac{1}{3}$ mile run by a participant, the sponsor will donate $\$5$. To calculate the total donation, we need to know the total distance covered by all the participants.

Calculating the Total Distance

Let's assume that there are $n$ participants, and each participant runs a certain distance. We can represent the total distance covered by all the participants as:

$$D = \sum_{i=1}^{n} d_i$$

where $d_i$ is the distance run by the $i^{th}$ participant.

Calculating the Total Donation

Now that we have the total distance covered by all the participants, we can calculate the total donation by multiplying the total distance by the donation amount per $\frac{1}{3}$ mile:

$$T = D \times \frac{\$5}{\frac{1}{3}}$$

Simplifying the expression, we get:

$$T = D \times \$15$$

Example Calculations

Let's consider an example to illustrate the calculation process. Suppose there are 5 participants, and each participant runs a distance of 3 miles. We can calculate the total distance covered by all the participants as:

$$D = 5 \times 3 = 15 \text{ miles}$$

Since the sponsor donates $\$5$ for every $\frac{1}{3}$ mile, we can calculate the total donation as:

$$T = 15 \times \frac{\$5}{\frac{1}{3}} = 15 \times \$15 = \$225$$

Answer Choices

Now that we have calculated the total donation, let's compare it with the answer choices:

• (a) $\$105$
• (b) $\$90$
• (c) $\$75$
• (d) $\$225$

Based on our calculation, the correct answer is:

• (d) $\$225$

Conclusion

In our previous article, we explored the calculation of the total donation made by a sponsor to a fundraiser. The sponsor donates $\$5$ for every $\frac{1}{3}$ mile that each participant runs. In this article, we will address some frequently asked questions related to this topic.

Q: How is the total donation calculated?

A: The total donation is calculated by multiplying the total distance covered by all the participants by the donation amount per $\frac{1}{3}$ mile. The formula for this calculation is:

$$T = D \times \frac{\$5}{\frac{1}{3}}$$

where $T$ is the total donation and $D$ is the total distance covered by all the participants.

Q: What is the donation amount per $\frac{1}{3}$ mile?

A: The donation amount per $\frac{1}{3}$ mile is $\$5$. This means that for every $\frac{1}{3}$ mile run by a participant, the sponsor will donate $\$5$.

Q: How is the total distance covered by all the participants calculated?

A: The total distance covered by all the participants is calculated by summing up the individual distances run by each participant. If there are $n$ participants, and each participant runs a distance of $d_i$, then the total distance is:

$$D = \sum_{i=1}^{n} d_i$$

Q: What if some participants do not complete the full distance?

A: If some participants do not complete the full distance, their individual distances will be subtracted from the total distance. For example, if a participant runs 2 miles instead of 3 miles, their distance will be subtracted from the total distance.

Q: Can the total donation be calculated if the number of participants is unknown?

A: Yes, the total donation can be calculated if the number of participants is unknown. In this case, the total distance covered by all the participants will be used to calculate the total donation.

Q: What if the donation amount per $\frac{1}{3}$ mile changes?

A: If the donation amount per $\frac{1}{3}$ mile changes, the total donation will also change. The new donation amount will be used to calculate the new total donation.

Q: Can the total donation be calculated if the individual distances are not known?

A: No, the total donation cannot be calculated if the individual distances are not known. In this case, the total distance covered by all the participants will be needed to calculate the total donation.

Q: What is the significance of the total donation?

A: The total donation is significant because it represents the amount of money that the sponsor will donate to the fundraiser. This amount can be used to support a good cause or to fund a specific project.

Conclusion

In conclusion, the total donation made by a sponsor to a fundraiser is calculated by multiplying the total distance covered by all the participants by the donation amount per $\frac{1}{3}$ mile. The total distance is calculated by summing up the individual distances run by each participant. The donation amount per $\frac{1}{3}$ mile is $\$5$. If the number of participants is unknown, the total distance will be used to calculate the total donation. If the donation amount per $\frac{1}{3}$ mile changes, the total donation will also change.