Rashon has $780 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 $481.28.
He buys 3 bicycle reflectors for $10.78 each and a pair of bike gloves for $32.64.
He plans to spend some or all of the money he has left to buy new biking outfits for $44.95 each.

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

Answer 1

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

1. Calculate the total spending on items already purchased:

   • Cost of the bicycle: $481.28
   • Cost of 3 reflectors: \(3 \times 10.78 = 32.34\)
   • Cost of bike gloves: $32.64

   Now, we add these amounts together:

   \[ \text{Total spending} = 481.28 + 32.34 + 32.64 \]

   Calculating this:

   \[ 481.28 + 32.34 = 513.62 \] \[ 513.62 + 32.64 = 546.26 \]

   Therefore, Rashon has spent a total of $546.26.

2. Calculate how much money is left:

   • Rashon started with $780, so the amount of money he has left is:

   \[ 780 - 546.26 = 233.74 \]

3. Define the inequality for the number of outfits ($o$) he can purchase:

   • Each biking outfit costs $44.95. The total cost for $o$ outfits will be \(44.95o\).
   • The amount of money Rashon has left must be greater than or equal to the cost of the outfits:

   \[ 44.95o \leq 233.74 \]

4. Solving the inequality:

   Divide both sides by 44.95:

   \[ o \leq \frac{233.74}{44.95} \]

   Now calculate the right-hand side:

   \[ \frac{233.74}{44.95} \approx 5.20 \]

   Since $o$ must be a whole number (he can only buy complete outfits), we round down to 5.

Thus, the final inequality is:

\[ o \leq 5 \]

This means Rashon can purchase at most 5 outfits with the remaining money he has.