Question

Answer the question.

You currently drive 288 miles per week in a car that gets 24 miles per gallon of gas. A
new fuel-efficient car costs $15,000 (after trade-in on your current car) and gets 48
miles per gallon. Insurance premiums for the new and old car are $800 and $600 per
year, respectively. You anticipate spending $1000 per year on repairs for the old car
and having no repairs on the new car. Assuming that gas remains at $3.50 per gallon,
estimate the number of years after which the costs of owning the new and old cars
are equal.
OA) 7.9 years
OB) 6.7 years
OC) 5.7 years
OD) 7.3 years

Answer 1

Answer: choice A 7.9 years

Explanation:

Set up the cost function

N(x) = (288*52 /48) * 3.5 * x + 15000 + 800x

Where N(x) is the cost of owning the new car over x years

O(x) = (288*52/24)* 3.5* x + 600x + 1000x

O(x) is the cost of owning ghe old car over x years

N(x) = 1092x +800x + 15000

N(x) = 1892x + 15000

O(x)= 2184x +600x +1000x

O(x) = 3784x

Set N(x) = O(x)

1892x +15000 = 3784x

1892x =15000

X= 15000/1892

X= 7.928 years

Choice A 7.9 years

From MysticAlanCheng