Tariq has $640 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.

He buys a new bicycle for $291.24.

He buys 4 bicycle reflectors for $19.56 each and a pair of bike gloves for $16.52.

He plans to spend some or all of the money he has left to buy new biking outfits for $50.80 each.

Write and solve an inequality which can be used to determine x*x*, the number of outfits Tariq can purchase while staying within his budget.

Let's start by calculating how much Tariq spends before purchasing any biking outfits:

1. **Cost of the bicycle**:  
   $ 291.24 $

2. **Cost of the 4 reflectors**:  
   Each reflector costs $ 19.56 $, so the total for 4 reflectors is:  
   \[
   4 \times 19.56 = 78.24
   \]

3. **Cost of the gloves**:  
   $ 16.52 $

Now, let's add these amounts together to find how much Tariq has spent so far:
\[
291.24 + 78.24 + 16.52 = 386.00
\]

Next, subtract this amount from the total budget of $640 to find how much money he has left for the biking outfits:
\[
640 - 386 = 254.00
\]

The cost of each biking outfit is $ 50.80 $. Let $ x $ represent the number of outfits Tariq can buy. The total cost of $ x $ outfits would be $ 50.80x $, and we know that this total must be less than or equal to the remaining money, which is $254.

Thus, the inequality that represents this situation is:
\[
50.80x \leq 254
\]

Now, solve for $ x $ by dividing both sides of the inequality by 50.80:
\[
x \leq \frac{254}{50.80} \approx 5
\]

Therefore, the maximum number of biking outfits Tariq can purchase is 5.

### Conclusion:
Tariq can buy up to **5 biking outfits** while staying within his budget.

Would you like more details or have any questions about this?

### Related Questions:
1. If Tariq decided to buy only 3 biking outfits, how much money would he have left?
2. How much would Tariq spend in total if he bought the maximum number of biking outfits?
3. What is the minimum number of biking outfits Tariq can buy if he wants to spend at least $200 on outfits?
4. How would the inequality change if each biking outfit cost $60 instead of $50.80?
5. If Tariq had only $500 to start with, what is the maximum number of biking outfits he could buy?

### Tip:
Always double-check calculations by re-adding totals to ensure no errors when working with multiple transactions!

Tariq has $640 to spend at a bicycle store for some new gear and biking outfits. He buys a new bicycle for $291.24. He buys 4 bicycle reflectors for $19.56 each and a pair of bike gloves for $16.52. He plans to spend some or all of the money he has left to buy new biking outfits for $50.80 each. Write and solve an inequality which can be used to determine x, the number of outfits Tariq can purchase while staying within his budget.

Learn how to solve an inequality to determine how many biking outfits Tariq can buy while staying within his $640 budget. This problem covers key mathematical concepts, including inequalities and budget calculations, suitable for students in Grades 6-8.

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