Alonso has $460 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.

Question

He buys a new bicycle for $270.71.
He buys 4 bicycle reflectors for $3.09 each and a pair of bike gloves for $33.71.
He plans to spend some or all of the money he has left to buy new biking outfits for $68.20 each.

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

Answer 1

To determine how many biking outfits Alonso can buy while staying within his budget, we first need to calculate how much money he has left after his initial purchases.

1. Alonso's total budget: $460

2. Cost of the new bicycle: $270.71

3. Cost of 4 bicycle reflectors: \[ 4 \times 3.09 = 12.36 \]

4. Cost of the pair of bike gloves: $33.71

5. Total cost of all items purchased: \[ \text{Total cost} = 270.71 + 12.36 + 33.71 = 316.78 \]

6. Amount left after purchases: \[ \text{Amount left} = 460 - 316.78 = 143.22 \]

7. Cost of each biking outfit: $68.20

Let \( x \) represent the number of biking outfits Alonso wants to buy. The total cost for \( x \) outfits is \( 68.20x \).

Now we can set up the inequality to determine how many outfits he can purchase without exceeding his remaining amount of money:

\[ 68.20x \leq 143.22 \]

Now, we can solve the inequality for \( x \):

To do this, we will divide both sides of the inequality by 68.20:

\[ x \leq \frac{143.22}{68.20} \]

Calculating the right side:

\[ \frac{143.22}{68.20} \approx 2.1 \]

Since \( x \) must be a whole number (he can't buy a fraction of an outfit), we take the largest whole number less than or equal to 2.1, which is 2.

Thus, the maximum number of biking outfits Alonso can purchase while staying within his budget is:

\[ \boxed{2} \]