To solve the question, let's carefully analyze the phrase provided: "The sum of the number of cats and 15 dogs."
Here are the steps:
1. Identify the variable for the number of cats, which is given as [tex]\( c \)[/tex].
2. Understand that the phrase "the sum of" indicates that we should add two quantities.
3. Recognize that the two quantities to be added are:
- The number of cats, represented by [tex]\( c \)[/tex].
- The number of dogs, which is specified as 15.
Therefore, the expression representing the sum of these two quantities is given by:
[tex]\[ c + 15 \][/tex]
Let's now evaluate the provided options:
- A. [tex]\( c + 15 \)[/tex]: This correctly represents the sum of the number of cats ([tex]\( c \)[/tex]) and 15 dogs.
- B. [tex]\( c - 15 \)[/tex]: This represents subtraction, not the sum.
- C. [tex]\( c \cdot 15 \)[/tex]: This represents multiplication.
- D. [tex]\( \frac{c}{15} \)[/tex]: This represents division.
The correct variable expression representing the phrase is:
[tex]\[ \boxed{c + 15} \][/tex]
