You have decided to join a walk-a-thon to raise money for the local animal shelter. There are two teams that you can join. Team A raises $5.50 per mile they walk. Team B raises $6.00 for entering the race, and then $4.00 for every mile they walk.

Now, solve for the number of dollars Team B raised per mile walked. Use the calculator to help you solve.

Team B
*d*=6+4*m*



Number of miles (*m*)Dollars raised (*d*)Dollars raised per mile (*md*​)

0

6.00

1

10.00

2

14.00

3

18.00

4

22.00

5

26.00

6

30.00

1234567890 - ,. 

Enter


For Team B, the total dollars raised ($d$) is calculated by the formula:
\[
d = 6 + 4m
\]
where:
- $6$ represents the fixed $6.00 entry fee.
- $4m$ represents $4.00 for every mile walked.

Now, let's complete the table for Team B based on this formula:

| Number of miles (m) | Dollars raised (d) | Dollars raised per mile ($ \frac{d}{m} $) |
|---------------------|--------------------|---------------------------------------------|
| 0                   | 6.00               | Undefined (no miles walked)                 |
| 1                   | 10.00              | $ \frac{10.00}{1} = 10.00 $               |
| 2                   | 14.00              | $ \frac{14.00}{2} = 7.00 $                |
| 3                   | 18.00              | $ \frac{18.00}{3} = 6.00 $                |
| 4                   | 22.00              | $ \frac{22.00}{4} = 5.50 $                |
| 5                   | 26.00              | $ \frac{26.00}{5} = 5.20 $                |
| 6                   | 30.00              | $ \frac{30.00}{6} = 5.00 $                |

### Analysis:

- At 0 miles, the dollars raised is $6.00 (from the entry fee).
- At 1 mile, the total dollars raised is $10.00, giving $10.00 per mile.
- As the number of miles increases, the dollars raised per mile gradually decreases because the fixed $6.00 entry fee gets spread out over more miles.

### Summary:
For Team B, the dollars raised per mile ($ \frac{d}{m} $) decreases as the number of miles walked increases, because the initial entry fee has less influence as more miles are walked.

Would you like to compare Team A and Team B for specific scenarios?

### Relative Questions:
1. At what number of miles does Team A raise more than Team B?
2. What happens to Team B’s earnings if they walk 10 miles?
3. How can you determine which team raises more money at different mile markers?
4. What is the total amount raised by Team B if they walk 8 miles?
5. How does the entry fee affect Team B’s overall strategy?

### Tip:
The fixed entry fee impacts Team B's dollars per mile more when fewer miles are walked. For higher distances, the per-mile contribution becomes more significant.

Learn how to calculate Team B's fundraising per mile for the walk-a-thon. Understand the formula d = 6 + 4m where d represents the dollars raised and m represents the number of miles walked. Explore how the entry fee and per-mile contribution affect the total fundraising amount. Suitable for students in Grades 6-8.

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