Company Alpha rents a compact car for $20 per day plus $0.09 per mile. Company Beta rents the same type of car for $29.5 per day plus $0.04 per mile. Suppose you want to rent a car from company Alpha for 5 days. How many miles can you drive the

car before it becomes more expensive than renting from Beta?

Alpha cost = 100 + .09 x

Beta cost = 147.50 + .04 x
so when is
100 + .09 x = 147.50 + .04 x

To find out how many miles you can drive the car before it becomes more expensive to rent from Company Alpha than from Company Beta, we need to compare the total cost of renting from Alpha for 5 days with the total cost of renting from Beta for the same duration.

Let's break down the cost for each company first:

Company Alpha:
- Daily rental cost: $20
- Cost per mile: $0.09

Company Beta:
- Daily rental cost: $29.5
- Cost per mile: $0.04

Now, let's calculate the total cost for each company over 5 days:

Company Alpha:
Total rental cost = (Daily rental cost x Number of days) + (Cost per mile x Number of miles)
= ($20 x 5) + ($0.09 x Number of miles)
= $100 + $0.09 x Number of miles

Company Beta:
Total rental cost = (Daily rental cost x Number of days) + (Cost per mile x Number of miles)
= ($29.5 x 5) + ($0.04 x Number of miles)
= $147.5 + $0.04 x Number of miles

Now, we need to find the number of miles at which the total cost of renting from Alpha is equal to the total cost of renting from Beta:

$100 + $0.09 x Number of miles = $147.5 + $0.04 x Number of miles

Rearranging this equation, we get:

$0.09 x Number of miles - $0.04 x Number of miles = $147.5 - $100

$0.05 x Number of miles = $47.5

Dividing both sides by $0.05, we find:

Number of miles = $47.5 / $0.05
= 950 miles

Therefore, you can drive the car from Company Alpha for up to 950 miles before it becomes more expensive than renting from Company Beta for a 5-day period.