To determine the equation that best represents Rodrigo's total pay in dollars, we need to factor in both his base pay and the commission he earns on his sales. Let's break this down step by step:
1. Base Pay: Rodrigo starts with a base pay of \$38,800. This is the fixed amount he earns regardless of his sales.
2. Commission: Rodrigo earns a 14% commission on his total sales. In decimal form, 14% can be written as 0.14.
3. Total Pay: The total pay [tex]\( y \)[/tex] that Rodrigo earns is the sum of his base pay and the commission on his sales.
If [tex]\( x \)[/tex] represents the total sales in dollars, then the commission Rodrigo earns from his sales is [tex]\( 0.14 \times x \)[/tex].
Therefore, his total pay is:
[tex]\[ y = \text{base pay} + \text{commission} \][/tex]
[tex]\[ y = 38800 + 0.14 \times x \][/tex]
Now we can choose the equation that correctly represents this relationship from the given options:
A. [tex]\( y = 38800 x + 0.14 \)[/tex]
- This incorrectly represents the equation. It incorrectly places [tex]\( 38800 \)[/tex] as a coefficient for [tex]\( x \)[/tex] and [tex]\( 0.14 \)[/tex] as a constant term.
B. [tex]\( y = 38800 + 0.014 x \)[/tex]
- This incorrectly represents the commission percentage as 0.014 instead of 0.14.
C. [tex]\( y = 38800 + 14 x \)[/tex]
- This incorrectly multiplies the total sales [tex]\( x \)[/tex] by 14 instead of the correct decimal commission rate of 0.14.
D. [tex]\( y = 38800 + 0.14 x \)[/tex]
- This correctly represents the equation for the total pay.
Therefore, the correct equation that represents Rodrigo's total pay is:
[tex]\[ \boxed{y = 38800 + 0.14 x} \][/tex]
