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].
