Ahmad will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
Costindollars
Milesdriven
OptionA
OptionB
(a)
If Ahmad drives the rental car 150 miles, which option costs less?
Option A
Option B
How much less does it cost than the other option?
$30
(b)
For what number of miles driven do the two options cost the same?
75
If Ahmad drives more than this amount, which option costs more?
Option A
Option B
Lacking data.
(A) option b $30 less
(a) If Ahmad drives the rental car 150 miles, Option A costs less than Option B. Option A costs $30 less than Option B.
(b) The two options cost the same for 75 miles driven. If Ahmad drives more than 75 miles, Option A would cost more than Option B.
To determine which option costs less for Ahmad if he drives 150 miles, we need to compare the costs of Option A and Option B for that mileage. The cost (in dollars) for each option depends on the miles driven.
The given information states that Option A costs $40 for every 100 miles driven, and Option B costs $25 for every 80 miles driven.
To calculate the cost of Option A for 150 miles, we will use the following formula:
Cost of Option A = (Cost per 100 miles) * (Miles driven / 100)
Cost of Option A = $40 * (150 / 100) = $40 * 1.5 = $60
To calculate the cost of Option B for 150 miles, we will use the following formula:
Cost of Option B = (Cost per 80 miles) * (Miles driven / 80)
Cost of Option B = $25 * (150 / 80) = $25 * 1.875 = $46.875 (approximately $46.88)
Therefore, Option A costs $60 and Option B costs approximately $46.88 for 150 miles.
Thus, Option B costs less than Option A for 150 miles. The difference in cost is:
Difference = Cost of Option A - Cost of Option B
Difference = $60 - $46.88 = $13.12 (approximately $13.12)
So, Option B costs $13.12 less than Option A for 150 miles.
Moving on to part (b), we need to find the number of miles driven where the two options cost the same. To do this, we can set up an equation and solve for the miles driven.
Let x be the number of miles driven where the two options cost the same.
For Option A:
Cost of Option A = $40 * (x / 100)
For Option B:
Cost of Option B = $25 * (x / 80)
To find the number of miles, we set the two equations equal to each other and solve:
$40 * (x / 100) = $25 * (x / 80)
Simplifying the equation:
40x / 100 = 25x / 80
Cross-multiplying, we get:
40x * 80 = 25x * 100
Simplifying further:
3200x = 2500x
Subtracting 2500x from both sides:
3200x - 2500x = 0
Solving for x:
700x = 0
x = 0
Therefore, the two options cost the same for 0 miles driven.
If Ahmad drives more than 0 miles, Option A will cost more than Option B.