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Chapter 4: Problem 52

Solve. $$ 789.23=0.25 \cdot q $$

Short Answer

Expert verified
q = 3156.92.

Step by step solution

01

Identify the Equation

The equation given is
02

Isolate the Variable

To isolate the variable \( q \), divide both sides of the equation by 0.25.
03

Perform the Division

Divide 789.23 by 0.25.
04

Calculate the Result

Using a calculator or manual division, the result is So, \(q = 3156.92\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equation Isolation
Equation isolation is a key step when solving linear equations. This involves getting the variable you are solving for by itself on one side of the equation. In our example, we are solving for the variable \( q \). The given equation is: \[ 789.23 = 0.25 \cdot q \].
To isolate \( q \), you need to undo the operation that is being performed on it. Here, \( q \) is being multiplied by 0.25. To undo this multiplication, we use division, the inverse operation of multiplication.
Division
In the context of isolating a variable, division is used to cancel out multiplication. To isolate \( q \), we divide both sides of the equation by the number that is multiplied by \( q \). Given the equation: \[ 789.23 = 0.25 \cdot q \]
We divide both sides by 0.25 to isolate \( q \): \[ \frac{789.23}{0.25} = q \].
This action effectively moves the 0.25 to the other side of the equation and leaves \( q \) by itself.
Algebra
Algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols; in our case, these symbols include numbers and variables. The primary goal is to solve for the unknowns, which are represented by variables like \( q \).
In the given example, we used simple algebraic steps. After isolating the variable \( q \), by dividing both sides by 0.25, we perform the calculation: \[ q = \frac{789.23}{0.25} = 3156.92 \].
Hence, \( q \) is determined to be 3156.92. Always remember, solving linear equations often involves performing inverse operations to isolate variables and solve for them.

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