Question

In Massachusetts, speeding fines are determined by the formula $$F=10(x-65)+50,$$ where $F$ is the cost, in dollars, of the fine if a person is caught driving $x$ miles per hour. Use this formula to solve. If a fine comes to $\$ 400,$ how fast was that person driving?

Name: Problem 88, Chapter 2: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-22T18:55:27-08:00
Duration: 1 min 36 s
Channel: Joshua Gullett
Description: In Massachusetts, speeding fines are determined by the formula F=10(x-65)+50, where F is the cost, in dollars, of the fine if a person is caught driving x miles per hour. Use this formula to solve. If a fine comes to 400, how fast was that person driving?

   In Massachusetts, speeding fines are determined by the formula
$$F=10(x-65)+50,$$
where $F$ is the cost, in dollars, of the fine if a person is caught driving $x$ miles per hour. Use this formula to solve.
If a fine comes to $\$ 400,$ how fast was that person driving?

Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer 4th Edition

Chapter 2, Problem 88

Instant Answer

Solved by Expert Joshua Gullett

06/22/2020

Step 1

We substitute $F$ with $400$ in the given formula $F=10(x-65)+50$ to get $$400=10(x-65)+50.$$ Show more…

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In Massachusetts, speeding fines are determined by the formula $$F=10(x-65)+50,$$ where $F$ is the cost, in dollars, of the fine if a person is caught driving $x$ miles per hour. Use this formula to solve. If a fine comes to $\$ 400,$ how fast was that person driving?

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Key Concepts

Linear Equations

Linear equations are algebraic equations in which the highest power of the variable is one. They typically follow the form y = mx + b, making it straightforward to solve for the variable by isolating it through inverse operations. This forms the basis of understanding relationships between variables and constants in a linear manner.

Algebraic Manipulation

Algebraic manipulation involves the use of arithmetic operations and properties of equality to simplify or rearrange equations. This process includes adding, subtracting, multiplying, or dividing both sides of an equation by the same number to isolate the variable of interest.

Solving for an Unknown

Solving for an unknown refers to the process of determining the value of a variable that satisfies an equation. In the context of linear equations, this involves isolating the variable on one side of the equation to find its numerical value using techniques like subtraction and division.

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