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:

Question

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?

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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

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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.