To determine the number of biking outfits \( x \) that Alonso can purchase while staying within his budget, we start with the total amount of money he has and subtract the amounts he has already spent.
- Initial Budget: Alonso has $460.
- Cost of Bicycle: He spends $270.71 on a new bicycle.
- Cost of Reflectors: He buys 4 reflectors at $3.09 each, which costs \( 4 \times 3.09 = 12.36 \).
- Cost of Gloves: He buys a pair of bike gloves for $33.71.
Now, let's calculate the total amount Alonso has spent so far.
\[ \text{Total spent} = \text{Cost of Bicycle} + \text{Cost of Reflectors} + \text{Cost of Gloves} \]
Substituting the values we have:
\[ \text{Total spent} = 270.71 + 12.36 + 33.71 \]
\[ \text{Total spent} = 316.78 \]
Next, we determine how much money he has left after these purchases.
\[ \text{Money Left} = 460 - 316.78 = 143.22 \]
Now we can express the amount he can spend on biking outfits. Each biking outfit costs $68.20. If he buys \( x \) outfits, the total cost for the outfits will be \( 68.20x \).
To stay within his budget, we set up the inequality:
\[ 68.20x \leq 143.22 \]
This inequality can be solved for \( x \) by dividing both sides by 68.20:
\[ x \leq \frac{143.22}{68.20} \]
Calculating the right side:
\[ x \leq 2.1 \]
Since \( x \) must be a whole number (he can't buy a fraction of an outfit), the largest whole number that satisfies this inequality is \( 2 \).
Final Inequality: \[ 68.20x \leq 143.22 \]
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