Question

A car rental company (company a) charges a flat fee of $20 per day plus $0.25 per mile driven. another car rental company (company b) charges a flat fee of $30 per day plus $0.20 per mile driven. for what number of miles driven will the two companies charge the same amount for a one-day rental? write an equation using the variable m for the number of miles to represent the situation. enter your answer in the box. solve the equation you wrote in the previous step. enter your answer in the box. m =

Answer 1

For a one-day rental, both car rental companies (Company A and Company B) will charge the same amount when the car is driven for 200 miles.

Step-by-step explanation:

To find the number of miles driven where both car rental companies charge the same amount, we can set up an equation with the variable m representing the number of miles driven. Company A charges $20 per day plus $0.25 per mile, so its cost is represented by the equation 20 + 0.25m. Company B charges $30 per day plus $0.20 per mile, so its cost is represented by the equation 30 + 0.20m. To find where the costs are equal, we set the two equations equal to each other:

20 + 0.25m = 30 + 0.20m

By solving for m, we subtract 0.20m from both sides, which gives us:

0.05m = 10

Then, we divide both sides by 0.05 to find the value of m:

m = 200

Therefore, both companies will charge the same amount for a one-day rental when the car is driven 200 miles.

Answer 2

To find the mileage where the rental costs from two different companies are equal, we create an equation for each and solve for the mileage. The breakeven point is found at 200 miles.

Step-by-step explanation:

To determine the number of miles driven, m, for which the charges of Company A and Company B are the same, we can set up an equation based on their charging policies. Company A's charges can be described by the equation Cost_A = 20 + 0.25m, and Company B's charges can be described by the equation Cost_B = 30 + 0.20m.

By setting Cost_A equal to Cost_B, we can find the breakeven point where both companies charge the same amount:

20 + 0.25m = 30 + 0.20m

To solve for m, we first subtract 0.20m from both sides:

0.05m = 10

Then, we divide both sides by 0.05 to isolate m:

m = 200

So the two companies will charge the same amount for a one-day rental when the car is driven 200 miles.