To determine the correct equation that models the wages of someone who makes [tex]$11.50 an hour, let us define the variables clearly:
- \( y \) represents the total earnings in dollars.
- \( x \) represents the hours worked.
Since the person earns $[/tex]11.50 for every hour worked, the relationship between the total earnings [tex]\( y \)[/tex] and the number of hours worked [tex]\( x \)[/tex] can be found by multiplying the hourly wage by the number of hours worked:
[tex]\[ y = 11.50 \cdot x \][/tex]
Now, let's examine each given option to see if it matches this relationship:
A. [tex]\( x = 1150 x \)[/tex]:
This equation does not make sense because it inaccurately represents the relationship and is not properly solving for total earnings [tex]\( y \)[/tex].
B. [tex]\( y = 1150 x \)[/tex]:
This equation suggests that the hourly wage is [tex]$1150, which is incorrect. The correct hourly wage is $[/tex]11.50.
C. [tex]\( x = 11.50 x \)[/tex]:
This equation is also incorrect, as it does not solve for total earnings [tex]\( y \)[/tex]. It confusingly states that hours worked equals 11.50 times the hours worked, which is mathematically inconsistent.
D. [tex]\( y = 11.50 x \)[/tex]:
This equation correctly shows that the total earnings [tex]\( y \)[/tex] are equal to the hourly wage $11.50 multiplied by the number of hours worked [tex]\( x \)[/tex], which accurately represents the scenario given in the problem.
Therefore, the correct equation is:
[tex]\[ y = 11.50 x \][/tex]
The correct choice is:
[tex]\[ \boxed{D: y = 11.50 x} \][/tex]
