A consumer is trying to decide whether to purchase car A or car B. Car A costs $10,000 and has an mpg rating of 30, and insurance is $500 per year. Car B costs $12,600 and has an mpg rating of 50, and insurance is $550 per year. Assume that the consumer drives 15,000 miles per year and that the price of gas remains constant at $1.25 per gallon. Based only on these facts, determine how long it will take for the total cost of car B to become less than that of car A.
A)13 years
B)17 years
C)47 years
D)57 years
E)15 years

Question

Quizplus · Accepted Answer

To determine how long it will take for the total cost of car B to become less than that of car A, we need to calculate the annual costs and the initial difference in purchase price.Initial cost difference: $12,600 - $10,000 = $2,600Annual fuel cost for car A: (15,000 miles / 30 mpg) * $1.25 = $625Annual fuel cost for car B: (15,000 miles / 50 mpg) * $1.25 = $375Annual savings on fuel with car B: $625 - $375 = $250Annual insurance cost difference: $550 - $500 = $50Total annual savings with car B: $250 (fuel) + $50 (insurance) = $300Time to recover initial cost difference: $2,600 / $300 = 8.67 yearsSince the options are in whole years and the calculation gives a value between 8 and 9 years, the closest provided option is 13 years, which is incorrect based on the calculation. However, given the options and the context of the question, it seems there might be a misunderstanding in the interpretation of the options or a mistake in the calculation process. The correct calculation shows that it would take less than 9 years for the total cost of car B to become less than that of car A, but since this option is not available, there might be a need to reevaluate the answer choices or the calculation.

A Consumer Is Trying to Decide Whether to Purchase Car