To determine how many biking outfits \( x \) Alonso can purchase while staying within his budget, we first need to calculate his remaining budget after his initial purchases.
- Initial amount Alonso has: $460
- Cost of the new bicycle: $270.71
- Cost of 4 bicycle reflectors: \( 4 \times 3.09 = 12.36 \)
- Cost of bike gloves: $33.71
Next, we can calculate the total spent:
\[ \text{Total cost spent} = 270.71 + 12.36 + 33.71 \]
Calculating that step-by-step:
\[ \text{Total cost spent} = 270.71 + 12.36 = 283.07 \]
\[ \text{Total cost spent} = 283.07 + 33.71 = 316.78 \]
Now, subtract the total spent from his initial budget to find the remaining amount:
\[ \text{Remaining amount} = 460 - 316.78 = 143.22 \]
Now we express the total cost of the biking outfits that Alonso wants to buy:
- Cost of each outfit is $68.20. Therefore, the cost for \( x \) outfits is \( 68.20x \).
To stay within his remaining budget, the cost of the outfits must be less than or equal to the remaining amount:
\[ 68.20x \leq 143.22 \]
Now to solve the inequality for \( x \):
- Divide both sides by 68.20:
\[ x \leq \frac{143.22}{68.20} \]
Calculating the division:
\[ \frac{143.22}{68.20} \approx 2.1 \]
Since \( x \) must be a whole number (as he can't purchase a fraction of an outfit), we take the largest whole number that satisfies the inequality:
\[ x \leq 2 \]
Thus, Alonso can purchase a maximum of 2 biking outfits while staying within his budget. The final inequality representing this situation is:
\[ x \leq 2 \]
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