What number divided by 3 then multiplied equals 24?
The Correct Answer and Explanation is :
To find the number that, when divided by 3 and then multiplied, equals 24, let’s set up an equation.
Let ( x ) be the unknown number.
- The problem states that dividing ( x ) by 3, then multiplying, results in 24.
- So, we can represent this as:
[
\frac{x}{3} \times 3 = 24
] - Simplifying this equation, we see that dividing ( x ) by 3 and then multiplying by 3 just returns ( x ):
[
x = 24
]
Thus, the answer is:
[
x = 24
]
Explanation
In this problem, we’re essentially trying to “undo” operations to find the original number. Let’s break down the steps:
- Setting Up the Equation: Since the problem describes dividing a number by 3 and then multiplying, we translate that into the algebraic form: (\frac{x}{3} \times 3).
- Understanding the Operations: Dividing a number by 3 and then immediately multiplying by 3 cancels out, leaving the original number. This works because multiplication and division by the same nonzero number are inverse operations.
- Solving the Equation: When (\frac{x}{3} \times 3 = 24), it simplifies directly to (x = 24). In other words, no matter the intermediate steps, if we end with 24, that means our original number, ( x ), must have been 24.
- Verification: To confirm, substitute 24 back into the problem’s steps. Dividing 24 by 3 gives 8, and multiplying 8 by 3 returns 24, which matches the expected outcome.
In summary, the number we’re looking for is 24, as it satisfies the condition laid out in the problem.