A truck can be rented from Company A for ​$150 a day plus ​$0.50 per mile. Company B charges ​$70 a day plus ​$0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same

To find the number of miles in a day at which the rental costs for Company A and Company B are the same, we need to set up an equation and solve for the number of miles.

Let's assume the number of miles in a day is represented by 'x'.

For Company A, the rental cost is calculated as follows:
Cost_A = $150 + $0.50x

For Company B, the rental cost is calculated as follows:
Cost_B = $70 + $0.90x

We can now set up an equation to find the number of miles at which the rental costs for Company A and Company B are the same:

Cost_A = Cost_B

$150 + $0.50x = $70 + $0.90x

Now, let's solve this equation for 'x':

$150 - $70 = $0.90x - $0.50x

$80 = $0.40x

Dividing both sides of the equation by $0.40:

$80 / $0.40 = x

200 = x

Therefore, the rental costs for Company A and Company B will be the same when the number of miles in a day is 200 miles.

To find the number of miles in a day at which the rental costs for Company A and Company B are the same, we can set up an equation based on the given information.

Let's assume the number of miles in a day is represented by 'm'.

For Company A, the rental cost can be calculated as follows:
Cost_A = 150 (flat daily rate) + 0.50 (price per mile) * m

For Company B, the rental cost can be calculated as follows:
Cost_B = 70 (flat daily rate) + 0.90 (price per mile) * m

Now, we can set up an equation to find the number of miles, 'm', where the rental costs are the same:
Cost_A = Cost_B

Plugging in the expressions for Cost_A and Cost_B, we have:
150 + 0.50m = 70 + 0.90m

To solve this equation, we can start by isolating 'm' on one side:
0.50m - 0.90m = 70 - 150
-0.40m = -80

Divide both sides of the equation by -0.40 to find the value of 'm':
m = (-80) / (-0.40)
m = 200

Therefore, the rental costs for Company A and Company B will be the same when the number of miles in a day is 200.

number of miles when it happens --- x

150 + .5m = 70 + .9m

solve for m