If taxi 1 charges 2.50 to ride and 20 cents for every 1/10 of a mile,

and taxi 2 charges 3.25 to ride and 15 cents for every 1/10 of a mile
at what point will they cost the same thing

just set up the expressions and solve for m miles (10m .1-mile segments):

2.50 + .20(10m) = 3.25 + .15(10m)

To find at what point the two taxis will cost the same amount, we need to set up an equation and solve for the distance traveled.

Let's suppose that the distance traveled is represented by 'x' in terms of tenths of a mile.

For taxi 1, the cost is $2.50 + $0.20 * x.
For taxi 2, the cost is $3.25 + $0.15 * x.

To find the point where they cost the same, we can set up an equation:

2.50 + 0.20x = 3.25 + 0.15x

Now, let's solve for 'x' to determine the distance at which the two taxis will cost the same:

2.50 + 0.20x - 0.15x = 3.25

0.05x = 3.25 - 2.50

0.05x = 0.75

x = 0.75 / 0.05

x = 15

Therefore, the two taxis will cost the same when the distance traveled is 15 tenths of a mile.