Car rental agency A charges $50 per day plus 10 cents per mile driven. Agency B charges $20 per day plus 30 cents per mile driven. For a one-day rental it is cheaper to rent from agency A if you drive more than?

the answer is 150

To determine when it is cheaper to rent from agency A, we need to compare the total cost of renting from each agency for a one-day rental.

For agency A:
Cost per day = $50
Cost per mile = $0.10

For agency B:
Cost per day = $20
Cost per mile = $0.30

Let's denote the number of miles driven in a one-day rental as M.

For agency A, the total cost can be calculated as:
Total cost for agency A = (Cost per day) + (Cost per mile * Miles driven)
Total cost for agency A = $50 + ($0.10 * M)

For agency B, the total cost can be calculated as:
Total cost for agency B = (Cost per day) + (Cost per mile * Miles driven)
Total cost for agency B = $20 + ($0.30 * M)

We want to find the point at which the total cost for agency A is cheaper than the total cost for agency B. In other words, we want to find the value of M for which:
Total cost for agency A < Total cost for agency B

$50 + ($0.10 * M) < $20 + ($0.30 * M)

Simplifying the equation:
$50 - $20 < ($0.30 * M) - ($0.10 * M)
$30 < $0.20 * M

Dividing both sides by $0.20:
$30 / $0.20 < M
150 < M

Therefore, if you drive more than 150 miles in a one-day rental, it is cheaper to rent from agency A.

x=24

50 + 10x = 20 + 30x

Solve for x.