The product of a number, x, and 0.28 is 13.44. Which equation matches this statement?
The correct answer and explanation is:
Correct Answer:
The correct equation that matches the given statement is: 0.28x=13.440.28x = 13.44
Explanation (300 words):
The problem states: “The product of a number, x, and 0.28 is 13.44.” Let’s break this sentence down carefully to understand the mathematical meaning behind it.
Step 1: Identify the Operation
The word “product” in mathematics refers to the result of a multiplication operation. Therefore, when the problem says “The product of a number, x, and 0.28”, it means we are multiplying x by 0.28.
So, we start with: Product=x×0.28\text{Product} = x \times 0.28
Step 2: Set Up the Equation
The statement continues: “…is 13.44.” The word “is” in math typically means equals. So, we replace “is” with the equal sign: x×0.28=13.44x \times 0.28 = 13.44
This is equivalent to: 0.28x=13.440.28x = 13.44
This equation matches the original sentence exactly, translating the language of the problem into a mathematical expression.
Step 3: Why This Equation Is Correct
Let’s check why this equation is valid. Suppose we want to find the value of xx. To solve the equation: 0.28x=13.440.28x = 13.44
We would divide both sides of the equation by 0.28: x=13.440.28=48x = \frac{13.44}{0.28} = 48
If we multiply 48 by 0.28, we get: 48×0.28=13.4448 \times 0.28 = 13.44
This confirms the equation is correct.
Conclusion:
The phrase “The product of a number, x, and 0.28 is 13.44” directly translates to the equation 0.28x = 13.44. This is the accurate and complete representation of the given word problem in algebraic form.