Let's work through the problem step-by-step to determine the inequality that represents the maximum number of biking outfits Luis can purchase while staying within his budget.
1. Calculate the total amount spent on initial items:
Luis buys:
- A new bicycle for \[tex]$209.67,
- 2 bicycle reflectors for \$[/tex]6.04 each,
- A pair of bike gloves for \[tex]$25.77.
First, calculate the total cost of the reflectors:
\[
\text{Total cost of reflectors} = 2 \times 6.04 = 12.08
\]
Next, calculate the initial total spent on the bicycle, reflectors and gloves:
\[
\text{Initial total spent} = 209.67 + 12.08 + 25.77 = 247.52
\]
2. Calculate the money left after purchasing the initial items:
\[
\text{Money left} = 420.00 - 247.52 = 172.48
\]
3. Represent the remaining budget as an inequality:
Let \( x \) be the number of biking outfits Luis can purchase. Each outfit costs \$[/tex]37.16.
The total cost of [tex]\( x \)[/tex] biking outfits is:
[tex]\[
37.16 \times x
\][/tex]
Adding this to the initial amount spent (\[tex]$247.52), we form the total expenditure:
\[
247.52 + 37.16x
\]
Since Luis has a total budget of \$[/tex]420.00, the inequality that represents this situation is:
[tex]\[
420 \geq 247.52 + 37.16x
\][/tex]
Therefore, the correct inequality to determine the maximum number of outfits Luis can purchase while staying within his budget is:
[tex]\[
420 \geq 37.16 x + 247.52
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{420 \geq 37.16 x + 247.52}
\][/tex]
