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Chapter 4: Problem 53

Solve. $$ 1048.8=23 \cdot t $$

Short Answer

Expert verified
t = 45.6

Step by step solution

01

Identify the equation

Write down the equation given in the problem: \[ 1048.8 = 23 \times t \]
02

Isolate the variable

To isolate the variable \( t \), divide both sides of the equation by 23: \[ t = \frac{1048.8}{23} \]
03

Calculate the division

Perform the division to find the value of \( t \): \[ t = 45.6 \]

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Key Concepts

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

Isolating Variables
Isolating the variable is an essential step in solving linear equations. In this problem, the goal is to solve for the variable 't'.
This means we need to get 't' by itself on one side of the equation.
We start with the equation:
\( 1048.8 = 23 \cdot t \)
To isolate 't', we divide both sides of the equation by 23.
This operation changes the equation to: \( t = \frac{1048.8}{23} \)
By dividing both sides by the number multiplying 't', we successfully isolate the variable, making 't' the subject of the equation.
This step is crucial as it simplifies the equation and leads us closer to the solution.
Division in Algebra
Division is one of the basic arithmetic operations used frequently in algebra.
In this problem, we use division to solve for the variable 't'.
The equation before isolation is:
\( 1048.8 = 23 \cdot t \)
To isolate 't', we divide both sides by 23:
\( t = \frac{1048.8}{23} \)
This step involves simple division where we calculate how many times 23 fits into 1048.8.
Algebraically, division undoes multiplication, helping to isolate variables.
Understanding division as a tool to reverse multiplication makes solving equations more intuitive.
Basic Math Operations
Mastering basic math operations is fundamental in algebra.
These operations include addition, subtraction, multiplication, and division.
In this problem, we primarily use multiplication and division:
- **Multiplication step**: Initially, the equation is \( 1048.8 = 23 \cdot t \). Here, 't' is multiplied by 23.
- **Division step**: We isolate 't' by dividing both sides by 23:
\( t = \frac{1048.8}{23} \). This step undoes the multiplication.

When applied correctly, these basics allow us to transform and solve equations efficiently. It is important to practice and become comfortable with these operations since they are foundational for more complex mathematics.

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