Question

EXCEL Moving charges moving truck rental rates based on how many miles the moving trucks are driven.  Their last 3 customers paid the following rates:

Ellen paid $59.84 for 88 miles

Ming paid $99.96 for 147 miles

Charles paid $21.76 for 32 miles

Part A:
How much does EXCEL Moving charge per mile?

Part B:
Advantage Truck Rental charges a $45.00 flat rate plus $0.38 per mile.  Aidan needs to rent a moving truck to travel 226 total miles.  Should Aidan rent a truck from Advantage or EXCEL?

​

Answer 1

To find out how EXCEL Moving charges per mile, we can determine the rate per mile for each of the last three customers and then find an average if necessary.

### Part A: Calculate EXCEL Moving charges per mile

**1. Calculate the rate per mile for each customer:**

- **Ellen:**
\[
\text{Rate} = \frac{\text{Total Cost}}{\text{Miles}} = \frac{59.84}{88} \approx 0.68
\]

- **Ming:**
\[
\text{Rate} = \frac{99.96}{147} \approx 0.68
\]

- **Charles:**
\[
\text{Rate} = \frac{21.76}{32} \approx 0.68
\]

Each calculation shows that the charge per mile is approximately \(0.68\) dollars (or 68 cents).

**EXCEL Moving's charge per mile:** **$0.68**

---

### Part B: Compare Aidan's costs with EXCEL Moving vs. Advantage Truck Rental

**1. Calculate EXCEL Moving’s total cost for Aidan:**
- **Miles:** 226 miles
- **Cost:**
\[
\text{Total Cost} = \text{Rate} \times \text{Miles} = 0.68 \times 226 \approx 153.68
\]

**2. Calculate Advantage Truck Rental’s total cost for Aidan:**
- **Flat Rate:** $45.00
- **Cost Per Mile:** $0.38
- **Total Miles:** 226
- **Total Cost:**
\[
\text{Total Cost} = \text{Flat Rate} + (\text{Cost Per Mile} \times \text{Miles}) = 45 + (0.38 \times 226) \approx 45 + 85.88 \approx 130.88
\]

### Conclusion:
- **Total cost at EXCEL Moving:** \$153.68
- **Total cost at Advantage Truck Rental:** \$130.88

Since **$130.88 (Advantage) < $153.68 (EXCEL)**, Aidan should **rent a truck from Advantage Truck Rental**.