To determine how many biking outfits Alonso can purchase while staying within his budget, we need to first find out how much money he has left after his initial purchases.
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Calculate the total cost of the initial purchases:
- Cost of the new bicycle: $270.71
- Cost of 4 bicycle reflectors at $3.09 each: \[ 4 \times 3.09 = 12.36 \]
- Cost of the pair of bike gloves: $33.71
Now, let's find the total cost of these items: \[ \text{Total cost} = 270.71 + 12.36 + 33.71 \]
Performing the addition: \[ 270.71 + 12.36 = 283.07 \] \[ 283.07 + 33.71 = 316.78 \]
So, the total cost of the bicycle and accessories is $316.78.
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Determine the remaining money: \[ \text{Remaining money} = 460 - 316.78 = 143.22 \]
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Express the cost of outfits in terms of the number of outfits (x): Each biking outfit costs $68.20, so if \( x \) is the number of outfits, the total cost for \( x \) outfits is: \[ 68.20x \]
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Set up the inequality: To stay within his budget, the cost of the outfits must be less than or equal to the remaining money: \[ 68.20x \leq 143.22 \]
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Solve the inequality for \( x \): \[ x \leq \frac{143.22}{68.20} \]
Now, perform the division: \[ x \leq 2.1 \]
Since \( x \) must be a whole number (you can't buy a fraction of an outfit), we take the largest whole number that satisfies the inequality:
Thus, the maximum number of outfits Alonso can purchase is 2.
Final inequality: \[ x \leq 2 \]
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