Stephanie is looking to purchase a used boat. She is choosing between two boats. The table shows information about each boat.
Boat A $2400 15 $600
Boat B $2800 18 $250
Stephanie wants to compare the total cost of buying and using these boats on her local lake.
• Stephanie estimates she will drive the boat at least 40 miles per month.
• The average cost of gasoline per gallon in her city is $3.89.
• Stephanie plans on owning the boat for 3 years.
Calculate and explain which boat will cost Stephanie the least to buy and use.
To calculate the total cost of buying and using each boat, we will need to consider the cost of buying the boat, the annual cost of insurance, and the annual cost of gasoline.
For Boat A:
- Cost of buying the boat: $2,400
- Annual cost of insurance: $600
- Annual cost of gasoline: 40 miles/month * 12 months/year * $3.89/gallon * 1 gallon/15 miles = $124
Total cost of buying and using Boat A for 3 years:
$2,400 + ($600 * 3) + ($124 * 3) = $8,232
For Boat B:
- Cost of buying the boat: $2,800
- Annual cost of insurance: $250
- Annual cost of gasoline: 40 miles/month * 12 months/year * $3.89/gallon * 1 gallon/18 miles = $106.67
Total cost of buying and using Boat B for 3 years:
$2,800 + ($250 * 3) + ($106.67 * 3) = $3,825.01
Based on the calculations, Boat B will cost Stephanie the least to buy and use, with a total cost of $3,825.01 compared to Boat A's total cost of $8,232.
To calculate the total cost of buying and using the boats, we need to consider the initial purchase price, the operating costs, and the ownership duration.
For Boat A:
- The initial purchase price is $2400.
- The estimated monthly mileage is 40 miles.
- Assuming an average fuel efficiency of 15 miles per gallon, Stephanie will require (40 miles / 15 miles per gallon) = 2.67 gallons of gasoline per month.
- The monthly fuel cost will be (2.67 gallons * $3.89 per gallon) = $10.40.
- The monthly operating cost (fuel cost) for Boat A will be $10.40.
- The annual operating cost for Boat A will be ($10.40 * 12 months) = $124.80.
- The total operating cost for 3 years will be ($124.80 * 3 years) = $374.40.
- The total cost of buying and using Boat A will be ($2400 + $374.40) = $2774.40.
For Boat B:
- The initial purchase price is $2800.
- The estimated monthly mileage is 40 miles.
- Assuming an average fuel efficiency of 18 miles per gallon, Stephanie will require (40 miles / 18 miles per gallon) = 2.22 gallons of gasoline per month.
- The monthly fuel cost will be (2.22 gallons * $3.89 per gallon) = $8.63.
- The monthly operating cost (fuel cost) for Boat B will be $8.63.
- The annual operating cost for Boat B will be ($8.63 * 12 months) = $103.56.
- The total operating cost for 3 years will be ($103.56 * 3 years) = $310.68.
- The total cost of buying and using Boat B will be ($2800 + $310.68) = $3110.68.
Therefore, Boat A will cost Stephanie the least to buy and use, with a total cost of $2774.40, compared to Boat B's total cost of $3110.68.
To calculate which boat will cost Stephanie the least to buy and use, we need to consider two main factors: the initial cost of purchasing the boat and the ongoing cost of using the boat.
Let's break down the costs for each boat:
Boat A:
- Purchase Price: $2400
- Fuel Consumption Rate: 15 miles per gallon
- Monthly mileage: 40 miles
- Cost of gasoline per gallon: $3.89
To calculate the fuel cost per month, we can divide the monthly mileage by the fuel consumption rate:
Fuel cost per month = (Monthly mileage) / (Fuel consumption rate)
Fuel cost per month = 40 miles / 15 miles per gallon
Fuel cost per month = 2.67 gallons
Next, we can multiply the fuel cost per month by the price of gasoline:
Fuel cost per month = 2.67 gallons * $3.89/gallon
Fuel cost per month = $10.37
Now, let's calculate the total cost of owning and using Boat A over 3 years:
Total fuel cost for 1 month = $10.37
Total fuel cost for 3 years = $10.37 * 12 months * 3 years = $372.12
Total cost of Boat A = Purchase Price + Total fuel cost for 3 years
Total cost of Boat A = $2400 + $372.12
Total cost of Boat A = $2772.12
Boat B:
- Purchase Price: $2800
- Fuel Consumption Rate: 18 miles per gallon
- Monthly mileage: 40 miles
- Cost of gasoline per gallon: $3.89
Following the same calculations as above, we can determine the total cost of owning and using Boat B over 3 years:
Total fuel cost for 1 month = $6.67
Total fuel cost for 3 years = $6.67 * 12 months * 3 years = $240
Total cost of Boat B = Purchase Price + Total fuel cost for 3 years
Total cost of Boat B = $2800 + $240
Total cost of Boat B = $3040
Comparing the total costs of Boat A and Boat B, we find that Boat A will cost Stephanie the least to buy and use. The total cost of Boat A over 3 years is $2772.12, while the total cost of Boat B is $3040. Therefore, Stephanie should choose Boat A if she wants to minimize her expenses.