Question

a speeding ticket in conroe costs $115 for the first 10 mi/h over the speed limit and $1 for each additional mi/h. in lakeville, a ticket costs $50 for the first 10 mi/h over the speed limit and $10 for each additional mi/h. if the speed limit is 55 mi/h, at what speed will the tickets cost approximately the same?

Answer 1

The speed = 72.22 mi/h when the tickets cost approximately the same.

Explanation:

It is given that, speeding ticket in control costs $115 for the first 10 mi/h over the speed limit and $1 for each additional mi/h.

Let the speed = x mi/h

Then, Overspeed cost = 115 + x - 65 = 50 + x → (1)

and Also, Overspeed Cost = 50 + (x -65)*10 = 10x - 600 → (2)

Solving equation (1) and (2), Step by step. We get,

10x - 600 = 50 + x

⇒ 10x -x = 50 +600

⇒ 9x = 650

⇒ x = 72.22 mi/h

Thus, the speed = 72.22 mi/h when the tickets cost approximately the same.

Answer 2

suppose the speed = x mi/h
Overspeed cost = 115 + x - 65 = 50 + x ....... 1
Overspeed Cost = 50 + (x -65)*10 = 10x - 600 ..........2
from [1] and [2], we get,
10x - 600 = 50 + x
10x -x = 50 +600
9x = 650
x = 72.22 mi/h
hope it helps