Question

Jim lives in a state in which speeders are fined $\$ 25$ for a speeding ticket plus $\$ 10$ for each mile per hour over the speed limit. Jim was given a ticket for $\$ 175$ for speeding in a 45 mile per hour zone. Which equation can be used to find how fast Jim was driving? (F) $45+(x-45) \cdot 10=175-25$ (G) $x-45 \cdot 10=175-25$ (h) $(x+45) \cdot 10=175-25$ (J) $(x-45) \cdot 10=175-25$

Name: Problem 23, Chapter 1: Algebra 1: Concepts and Skills
Uploaded: 2020-04-28T17:57:55-08:00
Duration: 1 min 14 s
Channel: Laura Skalaski
Description: Jim lives in a state in which speeders are fined 25 for a speeding ticket plus 10 for each mile per hour over the speed limit. Jim was given a ticket for 175 for speeding in a 45 mile per hour zone. Which equation can be used to find how fast Jim was driving? (F) 45+(x-45) ·10=175-25 (G) x-45 ·10=175-25 (h) (x+45) ·10=175-25 (J) (x-45) ·10=175-25

   Jim lives in a state in which speeders are fined $\$ 25$ for a speeding ticket plus $\$ 10$ for each mile per hour over the speed limit. Jim was given a ticket for $\$ 175$ for speeding in a 45 mile per hour zone. Which equation can be used to find how fast Jim was driving?
(F) $45+(x-45) \cdot 10=175-25$
(G) $x-45 \cdot 10=175-25$
(h) $(x+45) \cdot 10=175-25$
(J) $(x-45) \cdot 10=175-25$

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 1, Problem 23

Instant Answer

Solved by Expert Laura Skalaski

04/28/2020

Step 1

He was given a $175 ticket. So, we can write this as $25 + 10(x - 45) = 175$, where x is the speed at which Jim was driving. Show more…

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Jim lives in a state in which speeders are fined $\$ 25$ for a speeding ticket plus $\$ 10$ for each mile per hour over the speed limit. Jim was given a ticket for $\$ 175$ for speeding in a 45 mile per hour zone. Which equation can be used to find how fast Jim was driving? (F) $45+(x-45) \cdot 10=175-25$ (G) $x-45 \cdot 10=175-25$ (h) $(x+45) \cdot 10=175-25$ (J) $(x-45) \cdot 10=175-25$

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Key Concepts

Linear Equations

This concept involves understanding equations where variables appear with a constant coefficient, forming a straight-line graph when plotted. In problems like this, a fixed cost plus a per-unit increase can be modeled with a linear equation.

Translating Word Problems to Algebraic Equations

This key idea involves converting a written problem scenario into an algebraic equation by identifying constant values and variable components. The constant fee and the variable surcharge per unit of speed over the limit are represented algebraically.

Understanding Constant and Variable Components

In many real-world situations, parts of an expression remain fixed while other portions change depending on the situation. Recognizing that the fine consists of a base fee plus an additional fee based on how much the speed limit was exceeded is an example of identifying constant and variable parts in an equation.

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