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

First, let's calculate how much money Alonso has left after his purchases.

1. Cost of bicycle: $270.71
2. Cost of reflectors: \[ 4 \text{ reflectors} \times 3.09 \text{ each} = 4 \times 3.09 = 12.36 \]
3. Cost of bike gloves: $33.71

Now we can find the total amount spent by adding these costs together: \[ \text{Total spent} = 270.71 + 12.36 + 33.71 \] Calculating the total: \[ \text{Total spent} = 270.71 + 12.36 = 283.07 \] \[ \text{Total spent} = 283.07 + 33.71 = 316.78 \]

Now, we can find how much money Alonso has left to spend on biking outfits: \[ \text{Money left} = 460 - 316.78 = 143.22 \]

Now, let's define \( x \) as the number of biking outfits Alonso can purchase. Each outfit costs $68.20, so we can express the total cost for \( x \) outfits as: \[ 68.20x \]

To ensure Alonso stays within his budget, we need to set up the following inequality: \[ 68.20x \leq 143.22 \]

Now, let's solve for \( x \): \[ x \leq \frac{143.22}{68.20} \] Calculating the right side: \[ x \leq 2.1 \]

Since \( x \) must be a whole number (as he cannot purchase a fraction of an outfit), we round it down, which gives us: \[ x \leq 2 \]

Thus, the solution is that Alonso can buy at most 2 biking outfits while staying within his budget.

In summary, the inequality is: \[ 68.20x \leq 143.22 \]