Final answer:
To equate the costs of Jim's Taxi Company and Tammy's Taxis, you set up the equation $12 + $2x = $7 + $3x and solve for x, which represents the number of miles. The solution is x = 5, meaning the drive would need to be 5 miles for the costs to be the same.
Step-by-step explanation:
To find out how many miles it would take for the price of a ride to be the same for both Jim's Taxi Company and Tammy's Taxis, we can set up an equation based on the given pricing structures. Jim's Taxi Company charges a flat pick-up fee of $12 and then $2 a mile for the drive. Tammy's Taxis charge a flat fee of $7 and then $3 a mile for the drive. We let the number of miles driven be represented by x.
The equation to determine the equal cost point can be set up as follows:
Jim's Taxi: $12 + $2x = Tammy's Taxi: $7 + $3x
To solve for x, we rearrange the equation:
$2x - $3x = $7 - $12
- $1x = -$5
Now, divide both sides by -1:
x = 5
Thus, the drive would need to be 5 miles long for the cost to be the same for both companies.