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Chapter 3: Problem 73

Solve. $$ 48 \cdot t=1680 $$

Short Answer

Expert verified
t = 35

Step by step solution

01

Identify the Equation

Start by identifying the given equation: \[ 48 \times t = 1680 \]The goal is to solve for the variable t.
02

Isolate the Variable

To solve for t, isolate the variable on one side of the equation. Since t is currently multiplied by 48, divide both sides of the equation by 48: \[ t = \frac{1680}{48} \]
03

Simplify the Solution

Perform the division to get the value of t: \[ t = \frac{1680}{48} = 35 \]So, t equals 35.

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Key Concepts

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

Isolate the Variable
When solving a linear equation, the main goal is to find the value of the unknown variable. To do that, you need to isolate the variable on one side of the equation.
In the given problem, the variable is 't' in the equation: \(48 \times t = 1680\).
This means 't' is multiplied by 48. To isolate 't', you'll want to reverse the multiplication by dividing both sides of the equation by 48.
This step is crucial because it simplifies the equation and gives you the value of the variable: \(t = \frac{1680}{48}\).
By isolating the variable, we narrow down the equation to a simpler form that can be easily solved.
Division
Division plays a key role in solving linear equations, especially when a variable is being multiplied by a number.
In the equation \(48 \times t = 1680\), 't' is multiplied by 48. To cancel out the 48 and isolate 't', you divide both sides of the equation by 48.
Mathematically, this looks like: \(t = \frac{1680}{48}\).
Division is the opposite of multiplication and is used here to undo the multiplication. This makes it a powerful tool for solving equations.
Remember, whatever operation you do to one side of the equation, you must do to the other side as well to keep the equation balanced.
This principle is essential in maintaining the equality of the equation.
Simplification
Once you've isolated the variable using division, the next step is simplification. Simplification makes the equation easier to understand and solves for the exact value of the variable.
After dividing, you get \(t = \frac{1680}{48}\).
Performing the division: \(t = 35\).
Simplification removes any unnecessary complexity from the equation, making it simpler and more straightforward.
In this case, dividing 1680 by 48 gives us the simplified value of 't', which is 35.
Simplification is the final step and it ensures your answer is as clear and concise as possible.

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