9. Sophia is looking to purchase a used car. She is choosing between two cars. The table shows information about
each car.
Miles per Gallon
Estimated Repairs
20
Car
Car A
Car B
24
Sophia wants to compare the total cost of buying and using these cars.
Sophia estimates she will drive the car at least 50 miles per month,
The average cost of gasoline per gallon in her city is $3.99.
.
.
Cost
$8100
$8500
.
Sophia plans on owning the car for 4 years.
Which car will cost Sophia the least to buy and use? How much will the difference in cost be?
Car A will cost less for Sophia. The difference in cost will be $29.80.
Car B will cost less for Sophia. The difference in cost will be $29.80.
Car A will cost less for Sophia. The difference in cost will be $78.30.
Car B will cost less for Sophia. The difference in cost will be $78.30.
A.
B.
C.
D.
700
350
in dollars for parking hours at the marina.
Hours (h)
Total Cost

- Car A: $50 \text{ miles/month} \times \frac{12 \text{ months}}{1 \text{ year}} \times \frac{1}{20 \text{ miles/gallon}} \times \$3.99/\text{gallon}$

- Car B: $50 \text{ miles/month} \times \frac{12 \text{ months}}{1 \text{ year}} \times \frac{1}{24 \text{ miles/gallon}} \times \$3.99/\text{gallon}$

2. **Purchase Cost + 4 years of estimated repairs:**

- Car A: $8100 + 4 years of repairs

- Car B: $8500 + 4 years of repairs

Let me calculate these values to find out which car will cost Sophia the least.

For Car A:

Gasoline cost per year: $50 \text{ miles/month} \times 12 \text{ months/year} \times \frac{1}{20 \text{ miles/gallon}} \times \$3.99/\text{gallon} = \$119.70/year$

Total cost for 4 years:

$8100 + 4 \times 119.70 = 8100 + 478.80 = \$8578.80$

For Car B:

Gasoline cost per year: $50 \text{ miles/month} \times 12 \text{ months/year} \times \frac{1}{24 \text{ miles/gallon}} \times \$3.99/\text{gallon} = \$99.88/year$

Total cost for 4 years:

$8500 + 4 \times 99.88 = 8500 + 399.52 = \$8899.52$

So, the total cost for Car A over 4 years is \$8578.80 and for Car B is \$8899.52.

Therefore, Car A will cost Sophia less by:

$8899.52 - 8578.80 = \$320.72$

The correct answer is D. Car A will cost less for Sophia, and the difference in cost will be $320.72.