Question

Use the following information. Jeff lives in a state in which speeders are fined \(\$ 20\) for each mile per hour (mi/h) over the speed limit. Jeff was given a ticket for \(\$ 260\) for speeding on a road where the speed limit is 45 miles per hour. Jeff wants to know how fast he was driving. Use the labels to translate the verbal model into an algebraic model.

Short answer

Jeff was driving at 58 miles per hour when he was fined.

Step-by-step solution

Convert the Verbal Model into an Algebraic Model

Let's denote Jeff's speed as \(S\), and the speed over the limit he was driving as \(x\). According to the problem, Jeff was fined $20 for each mile per hour over the speed limit, which results in a fine of $260. This can be converted into the equation: \(20*x = 260\).

Solve for x

Solving the equation from Step 1 for \(x\) gives: \(x = \frac{260}{20} = 13\). This means that Jeff was driving 13 miles per hour over the speed limit.

Find Jeff's speed

Knowing the amount by which Jeff exceeded the speed limit, we can find his actual speed: \(S = 45 + 13 = 58\) miles per hour. Therefore, Jeff was driving at a speed of 58 miles per hour when he got the ticket.