Let's analyze the problem step by step to determine the correct equation that represents Cora's total pay.
Cora earns:
1. A base pay of [tex]\(\$ 58,400\)[/tex]
2. A commission of [tex]\(11\%\)[/tex] on her total sales [tex]\(x\)[/tex].
We need to create an equation [tex]\(y\)[/tex] that represents her total pay in dollars.
### Step-by-Step Solution
1. Base Pay:
- Cora earns a fixed base salary of [tex]\(\$ 58,400\)[/tex].
- This amount does not change regardless of her sales volume.
2. Commission:
- Commission is a percentage of her total sales ([tex]\(x\)[/tex]).
- The commission rate is [tex]\(11\%\)[/tex].
- This can be represented mathematically as [tex]\(0.11 \times x\)[/tex].
3. Total Pay Equation:
- To find the total pay [tex]\(y\)[/tex], we sum up the base pay and the commission on sales.
- So, the equation becomes:
[tex]\[
y = 58400 + 0.11x
\][/tex]
Now let's review the options provided:
A) [tex]\( y = 58400 + 0.011x \)[/tex]
- This equation implies a commission rate of [tex]\(1.1\%\)[/tex], which is incorrect.
B) [tex]\( y = 58400x + 0.11 \)[/tex]
- This option incorrectly represents a product of the base salary and total sales, which makes no sense contextually.
C) [tex]\( y = 58400 + 0.11x \)[/tex]
- This is exactly what we derived: a base pay of [tex]\(\$ 58,400\)[/tex] plus a [tex]\(11\%\)[/tex] commission on total sales [tex]\(x\)[/tex].
D) [tex]\( y = 58400 + 11x \)[/tex]
- This equation suggests a commission rate of [tex]\(1100\%\)[/tex], which is incorrect.
Therefore, the correct equation from the given options is:
[tex]\[ \boxed{C: \, y = 58400 + 0.11x} \][/tex]
This equation accurately represents Cora's total pay considering both her base salary and the commission from her sales.
