To find the total expenses Petra incurred for the car after 6 months, we need to consider the cost of the car, the registration fee, and the insurance cost for six months. Let's break down each component step-by-step.
1. Car Cost: This is the initial purchase price of the car.
[tex]\[
\$19,600
\][/tex]
2. Registration Fee: This is a one-time fee associated with the registration of the car.
[tex]\[
\$425
\][/tex]
3. Insurance: The insurance cost is a recurring expense, and Petra pays \[tex]$45 per month. Given we need the cost for 6 months, we calculate the total insurance cost over this period.
- Monthly insurance cost: \$[/tex]45
- Number of months: 6
- Total insurance cost:
[tex]\[
45 \, \text{dollars/month} \times 6 \, \text{months} = \$270
\][/tex]
4. Total Cost Calculation: Add up all individual costs to get the total expenses after 6 months.
[tex]\[
\text{Total cost} = \text{Car cost} + \text{Registration fee} + \text{Total insurance cost}
\][/tex]
[tex]\[
\text{Total cost} = 19,600 + 425 + 270 = 20,295
\][/tex]
Therefore, the total expenses for the car after 6 months is:
[tex]\[
\$20,295
\][/tex]
So, the correct answer is:
[tex]\[
\$20,295
\][/tex]
