Let's carefully break down the given word description: "The quotient of four and the sum of a number and three."
1. Quotient means division – We need to divide one quantity by another.
2. Four – This is the numerator of our division.
3. The sum of a number and three – This sum forms the denominator of our division.
Now let's translate these parts into an algebraic expression step-by-step:
- We represent the unknown number as [tex]\( x \)[/tex].
- The sum of this number and three is written as [tex]\( x + 3 \)[/tex].
- The quotient of four and this sum is represented as [tex]\(\frac{4}{x+3}\)[/tex].
Now to match this expression with the given choices:
A. [tex]\(\frac{x+3}{4}\)[/tex] – This option reverses the correct quotient.
B. [tex]\(\frac{x}{4}+3\)[/tex] – Here, only [tex]\( x \)[/tex] is divided by 4, and then 3 is added, which doesn't match our description.
C. [tex]\(\frac{4}{x+3}\)[/tex] – This matches our derived expression perfectly.
D. [tex]\(\frac{4}{x}+3\)[/tex] – This incorrectly adds 3 after dividing 4 by [tex]\( x \)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{3}
\][/tex]
