City Cab Company charges $3.50 a ride plus $2.00 per mile traveled. Metro Cab Company charges $1.50 a ride plus $2.50 per mile traveled. Write and solve an equation to find the number of miles for which the total cost is the same for both taxi companies.
3.50 + 2.00x = 1.50 + 2.50x
Now just solve for x
Sure, let's call the number of miles traveled "m".
For City Cab Company, the total cost would be:
3.50 + 2.00m
For Metro Cab Company, the total cost would be:
1.50 + 2.50m
So, we want to find the value of "m" for which these two expressions are equal:
3.50 + 2.00m = 1.50 + 2.50m
Let's solve this equation:
First, let's simplify:
3.50 - 1.50 = 2.50m - 2.00m
2.00 = 0.50m
Next, let's isolate "m" by dividing both sides of the equation by 0.50:
m = 4
Therefore, the number of miles for which the total cost is the same for both taxi companies is 4 miles.
Let's assume the number of miles traveled is 'x'.
For City Cab Company:
Total cost = $3.50 + $2.00 * x
For Metro Cab Company:
Total cost = $1.50 + $2.50 * x
To find the number of miles for which the total cost is the same for both taxi companies, we can set up an equation:
$3.50 + $2.00 * x = $1.50 + $2.50 * x
Now, let's solve the equation:
$2.00 * x - $2.50 * x = $1.50 - $3.50
- $0.50 * x = - $2.00
Dividing both sides by - $0.50:
x = $2.00 / $0.50
x = 4
Therefore, the number of miles for which the total cost is the same for both taxi companies is 4 miles.
To find the number of miles for which the total cost is the same for both taxi companies, we can set up an equation.
Let's assume the total cost for City Cab Company after traveling x miles is C1, and the total cost for Metro Cab Company after traveling x miles is C2.
For City Cab Company, the total cost consists of a fixed charge of $3.50 plus a charge of $2.00 per mile traveled. So, the equation for City Cab Company is:
C1 = 3.50 + 2.00x
For Metro Cab Company, the total cost consists of a fixed charge of $1.50 plus a charge of $2.50 per mile traveled. So, the equation for Metro Cab Company is:
C2 = 1.50 + 2.50x
Now, we can set C1 equal to C2 to find the number of miles for which the total cost is the same:
3.50 + 2.00x = 1.50 + 2.50x
To solve this equation, we need to isolate x. Subtracting 1.50 from both sides and subtracting 2.00x from both sides, we get:
3.50 - 1.50 = 2.50x - 2.00x
2.00 = 0.50x
Dividing both sides by 0.50, we find:
x = 4
Therefore, the total cost will be the same for both taxi companies when the number of miles traveled is 4 miles.