Let's work through the information provided to find the correct equation that models Hattie's total pay [tex]\(y\)[/tex] in dollars, based on the number of hours [tex]\(x\)[/tex] that she works.
1. Signing Bonus:
Hattie receives a one-time signing bonus of \[tex]$550.
2. Hourly Rate:
Hattie earns \$[/tex]32 per hour.
To model Hattie's total pay [tex]\(y\)[/tex], we need to consider both her signing bonus and the amount she earns based on her hours of work.
Here is how we can set up the equation step-by-step:
1. Total Amount Earned from Hours Worked:
If Hattie works [tex]\(x\)[/tex] hours and earns \[tex]$32 per hour, the total earnings from her working hours can be calculated as:
\[
32x
\]
2. Total Pay Calculation:
To find Hattie's total pay \(y\), we need to add her signing bonus (\$[/tex]550) to her earnings from the hours worked. This gives us the complete equation:
[tex]\[
y = 32x + 550
\][/tex]
Now we compare this derived equation with the given choices:
A. [tex]\(y = 550x - 32\)[/tex]
B. [tex]\(y = 32x - 550\)[/tex]
C. [tex]\(y = 32x + 550\)[/tex]
D. [tex]\(y = 550x + 32\)[/tex]
The correct option, which matches our derived equation, is:
C. [tex]\(y = 32x + 550\)[/tex]
So, the correct equation that models Hattie's total pay is:
[tex]\[
y = 32x + 550
\][/tex]
