Select the correct answer.

Charlotte has been working for her company for [tex][tex]$x$[/tex][/tex] years. The number of years Travis has been working for the same company, [tex][tex]$y$[/tex][/tex] years, is exactly 3 years longer than Charlotte.

What is the range of the relationship between [tex][tex]$x$[/tex][/tex] and [tex][tex]$y$[/tex][/tex]?
A. [tex][tex]$y \geq 0$[/tex][/tex]
B. [tex][tex]$y \geq 3$[/tex][/tex]
C. [tex][tex]$y \leq 3$[/tex][/tex]
D. [tex][tex]$0 \leq y \leq 3$[/tex][/tex]



Answer :

Let's carefully examine the relationship between Charlotte's and Travis's years of service.

1. Understand the problem statement:
- Charlotte has been working for a certain number of years, which we denote by [tex]\( x \)[/tex].
- Travis has been working for precisely 3 years longer than Charlotte.

2. Define the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- Given that Travis has been working 3 years more than Charlotte, we can express his years of service, [tex]\( y \)[/tex], as:
[tex]\[ y = x + 3 \][/tex]

3. Determine the range of [tex]\( y \)[/tex]:
- Since [tex]\( y \)[/tex] is defined as [tex]\( x + 3 \)[/tex], let's consider what this implies about the possible values of [tex]\( y \)[/tex].
- Regardless of the value of [tex]\( x \)[/tex] (as long as [tex]\( x \geq 0 \)[/tex] because the number of years worked cannot be negative), [tex]\( y \)[/tex] will always be greater than or equal to 3 (since [tex]\( y \)[/tex] is always adding 3 to [tex]\( x \)[/tex]).

4. State the conclusion:
- Therefore, the proper condition representing the range of [tex]\( y \)[/tex] can be described by the inequality:
[tex]\[ y \geq 3 \][/tex]

Hence, the correct answer is:

B. [tex]\( y \geq 3 \)[/tex]