Question4. Based on the information provided below:
\begin{tabular}{ll}
\begin{tabular}{l}
Loan Payment, \$6,625 \\
18,400
\end{tabular} & Annual mileage, \\
Insurance, \$2,160 & Miles per gallon, 26 \\
\begin{tabular}{l}
Parking/Tolls, \$375 \\
fees, \$58
\end{tabular} & License/Registration
\end{tabular}
Average gasoline price, per gallon Oil Changes/Repairs, \$425
a. Calculate the total annual operating cost for this car.
b. Calculate the operating cost per mile. (round to 4 decimals)
Studdy Solution
STEP 1
What is this asking? We need to find the total yearly cost of owning and running this car, and then figure out how much it costs per mile driven. Watch out! Don't forget to convert the given information into the correct units (yearly costs) before adding everything up!
STEP 2
1. Calculate the annual fuel cost.
2. Calculate the total annual operating cost.
3. Calculate the operating cost per mile.
STEP 3
Alright, so let's **start** by figuring out how much is spent on gas each year!
We know this car gets **26 miles per gallon** and that gas costs **\$3.25 per gallon**.
STEP 4
To find the annual fuel cost, we first need the **annual mileage**, which is **18,400 miles**.
Now, let's divide the **annual mileage** by the **miles per gallon** to find out how many gallons of gas are used in a year:
So, this car uses approximately **707.69 gallons** of gas per year.
STEP 5
Now, we can multiply the number of gallons used by the price per gallon: That means the annual fuel cost is **\$2,298.99**!
STEP 6
Now for the grand total!
We'll add up all the individual costs.
Remember, we're looking for *annual* costs, so make sure everything is in terms of years.
STEP 7
Let's list out all the **annual costs**: * **Loan Payment:** 6,625 * **Insurance:** 2,160 * **Parking/Tolls:** 375 * **License/Registration:** 58 * **Fuel Cost:** 2,298.99 (calculated in the previous step) * **Oil Changes/Repairs:** 425
STEP 8
Adding all these costs together gives us: So, the **total annual operating cost** is 11,941.99!
STEP 9
Almost there!
Now, we just need to figure out the cost *per mile*.
We have the **total annual operating cost** (11,941.99) and the **annual mileage** (18,400 miles).
STEP 10
Let's divide the **total annual operating cost** by the **annual mileage**: Rounding to four decimal places, we get **\$0.6489 per mile**.
STEP 11
a. The total annual operating cost for this car is **\$11,941.99**. b. The operating cost per mile is **\$0.6489**.
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