Question

An insurance company is considering implementing a plan based on mileage. The current plan, Plan A, charges a flat rate of $268.00 per month. Plan B charges a flat rate of $178.40 per month plus an additional $0.08 per mile driven the previous month. Using the inequality below, find the number of miles, x, where the cost of Plan B is less than the cost of Plan A.

A) x < 1500
B) x > 1500
C) x = 1500
D) x = 1680

Answer 1

To find when Plan B is cheaper than Plan A, solve the inequality 178.40 + 0.08x < 268.00 for x. The solution is x < 1120, which indicates that for any number of miles less than 1500, Plan B is less expensive than Plan A. Therefore, the correct answer is A) x < 1500.

Step-by-step explanation:

To determine the number of miles, x, where the cost of Plan B is less than the cost of Plan A, we can set up the following inequality:

178.40 + 0.08x < 268.00

To solve for x, we subtract 178.40 from both sides of the inequality:

0.08x < 268.00 - 178.40
0.08x < 89.60
Next, we divide both sides by 0.08 to isolate x:

x < \frac{89.60}{0.08}
x < 1120

Therefore, when a driver drives less than 1120 miles, Plan B will cost less than Plan A. The correct answer would be A) x < 1500 miles, which means that for any amount of miles less than 1500, Plan B is the cheaper option.