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The product of two numbers, [tex]\(x\)[/tex] and [tex]\(x+3\)[/tex], is 550. Which equation could be solved to find the value of the smaller number, [tex]\(x\)[/tex]?

A. [tex]\(x^2 + 3x = 550\)[/tex]

B. [tex]\(x^2 + 3 = 550\)[/tex]

C. [tex]\(3x + 3 = 550\)[/tex]

D. [tex]\(3x^2 = 500\)[/tex]



Answer :

GinnyAnswer
Let's break down the problem step by step to find the equation that can be solved to determine the value of the smaller number [tex]\( x \)[/tex].

1. Define the Variables:
- Let [tex]\( x \)[/tex] be the smaller number.
- The larger number is consequently [tex]\( x + 3 \)[/tex].

2. Setup the Problem:
- According to the problem, the product of these two numbers is 550. Therefore, the equation can be written as:
[tex]\[ x \cdot (x + 3) = 550 \][/tex]

3. Expand and Simplify the Equation:
- Distribute [tex]\( x \)[/tex] to both terms inside the parentheses:
[tex]\[ x \cdot x + x \cdot 3 = 550 \][/tex]
[tex]\[ x^2 + 3x = 550 \][/tex]

4. Formulate the Standard Form:
- The equation now is:
[tex]\[ x^2 + 3x - 550 = 0 \][/tex]

Let's now look at the given options and identify which one matches the equation derived.

A. [tex]\( x^2 + 3x = 550 \)[/tex]

B. [tex]\( x^2 + 3 = 550 \)[/tex]

C. [tex]\( 3x + 3 = 550 \)[/tex]

D. [tex]\( 3x^2 = 500 \)[/tex]

From the steps outlined, we see that the correct equation is given by option:

A. [tex]\( x^2 + 3x = 550 \)[/tex]

This is the equation that can be solved to find the value of the smaller number [tex]\( x \)[/tex].

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