The total cost of the two options will be the same after 2 miles. When the two options are the same, the price will be $7.
To find the point at which the total cost of the two options will be the same, we can set up an equation to represent the total cost for each option and then solve for the number of miles.
Let's denote the number of miles as "m". The total cost for Option A (taxi) is given by the equation:
[ y_A = 5 + 1m ]
The total cost for Option B (Uber) is given by the equation:
[ y_B = 3 + 2m ]
To find the point at which the total cost of the two options will be the same, we can set up the equation:
[ 5 + 1m = 3 + 2m ]
Solving for "m", we get:
[ 5 - 3 = 2m - 1m ]
[ 2 = m ]
So, the total cost of the two options will be the same after 2 miles.
To find the price at this point, we can substitute "m = 2" into either of the total cost equations. Let's use the equation for Option A (taxi):
[ y_A = 5 + 1(2) ]
[ y_A = 5 + 2 ]
[ y_A = 7 ]
Therefore, when the two options are the same, the price will be $7.