Question John has \( \$ 700 \) 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 \( \$ 466.89 \). - He buys 2 bicycle reflectors for \( \$ 11.16 \) each and a pair of bike gloves for \( \$ 24.38 \). - He plans to spend some or all of the money he has left to buy new biking outfits for \( \$ 44.52 \) each. Which inequality can be used to determine \( o \), the maximum number of outfits John can purchase while staying within his budget?

To determine the maximum number of biking outfits \( o \) that John can purchase while staying within his budget, we need to set up an inequality based on his total spending. 1. **Known Conditions:** - Total budget: \( 700 \) - Cost of the bicycle: \( 466.89 \) - Cost of 2 bicycle reflectors: \( 2 \times 11.16 = 22.32 \) - Cost of bike gloves: \( 24.38 \) - Cost of each biking outfit: \( 44.52 \) 2. **Calculate Total Spending on Current Purchases:** - Total spent on bicycle, reflectors, and gloves: \[ \text{Total spent} = 466.89 + 22.32 + 24.38 \] 3. **Calculate Remaining Budget:** - Remaining budget after these purchases: \[ \text{Remaining budget} = 700 - \text{Total spent} \] 4. **Set Up the Inequality:** - The cost of \( o \) outfits is \( 44.52o \). - The inequality representing the remaining budget after purchasing outfits is: \[ \text{Remaining budget} \geq 44.52o \] Now, let's calculate the total spent and the remaining budget to finalize the inequality. ### Step 1: Calculate Total Spent \[ \text{Total spent} = 466.89 + 22.32 + 24.38 \] ### Step 2: Calculate Remaining Budget \[ \text{Remaining budget} = 700 - \text{Total spent} \] ### Step 3: Set Up the Inequality \[ 700 - \text{Total spent} \geq 44.52o \] Now, let's perform the calculations. Calculate the value by following steps: - step0: Calculate: \(466.89+22.32+24.38\) - step1: Add the numbers: \(513.59\) Calculate or simplify the expression \( 700 - (466.89 + 22.32 + 24.38) \). Calculate the value by following steps: - step0: Calculate: \(700-\left(466.89+22.32+24.38\right)\) - step1: Add the numbers: \(700-513.59\) - step2: Subtract the numbers: \(186.41\) ### Step 1: Calculate Total Spent The total amount John has spent on the bicycle, reflectors, and gloves is: \[ \text{Total spent} = 466.89 + 22.32 + 24.38 = 513.59 \] ### Step 2: Calculate Remaining Budget The remaining budget after these purchases is: \[ \text{Remaining budget} = 700 - 513.59 = 186.41 \] ### Step 3: Set Up the Inequality Now we can set up the inequality to determine the maximum number of outfits \( o \) that John can purchase: \[ 186.41 \geq 44.52o \] ### Final Inequality To express this in a standard form, we can rearrange it: \[ 44.52o \leq 186.41 \] This inequality can be used to determine \( o \), the maximum number of outfits John can purchase while staying within his budget.