Answer :
Let's work through the problem step-by-step to determine the inequality that represents the maximum number of biking outfits Luis can purchase while staying within his budget.
1. Calculate the total amount spent on initial items:
Luis buys:
- A new bicycle for \[tex]$209.67, - 2 bicycle reflectors for \$[/tex]6.04 each,
- A pair of bike gloves for \[tex]$25.77. First, calculate the total cost of the reflectors: \[ \text{Total cost of reflectors} = 2 \times 6.04 = 12.08 \] Next, calculate the initial total spent on the bicycle, reflectors and gloves: \[ \text{Initial total spent} = 209.67 + 12.08 + 25.77 = 247.52 \] 2. Calculate the money left after purchasing the initial items: \[ \text{Money left} = 420.00 - 247.52 = 172.48 \] 3. Represent the remaining budget as an inequality: Let \( x \) be the number of biking outfits Luis can purchase. Each outfit costs \$[/tex]37.16.
The total cost of [tex]\( x \)[/tex] biking outfits is:
[tex]\[ 37.16 \times x \][/tex]
Adding this to the initial amount spent (\[tex]$247.52), we form the total expenditure: \[ 247.52 + 37.16x \] Since Luis has a total budget of \$[/tex]420.00, the inequality that represents this situation is:
[tex]\[ 420 \geq 247.52 + 37.16x \][/tex]
Therefore, the correct inequality to determine the maximum number of outfits Luis can purchase while staying within his budget is:
[tex]\[ 420 \geq 37.16 x + 247.52 \][/tex]
So, the correct choice is:
[tex]\[ \boxed{420 \geq 37.16 x + 247.52} \][/tex]
1. Calculate the total amount spent on initial items:
Luis buys:
- A new bicycle for \[tex]$209.67, - 2 bicycle reflectors for \$[/tex]6.04 each,
- A pair of bike gloves for \[tex]$25.77. First, calculate the total cost of the reflectors: \[ \text{Total cost of reflectors} = 2 \times 6.04 = 12.08 \] Next, calculate the initial total spent on the bicycle, reflectors and gloves: \[ \text{Initial total spent} = 209.67 + 12.08 + 25.77 = 247.52 \] 2. Calculate the money left after purchasing the initial items: \[ \text{Money left} = 420.00 - 247.52 = 172.48 \] 3. Represent the remaining budget as an inequality: Let \( x \) be the number of biking outfits Luis can purchase. Each outfit costs \$[/tex]37.16.
The total cost of [tex]\( x \)[/tex] biking outfits is:
[tex]\[ 37.16 \times x \][/tex]
Adding this to the initial amount spent (\[tex]$247.52), we form the total expenditure: \[ 247.52 + 37.16x \] Since Luis has a total budget of \$[/tex]420.00, the inequality that represents this situation is:
[tex]\[ 420 \geq 247.52 + 37.16x \][/tex]
Therefore, the correct inequality to determine the maximum number of outfits Luis can purchase while staying within his budget is:
[tex]\[ 420 \geq 37.16 x + 247.52 \][/tex]
So, the correct choice is:
[tex]\[ \boxed{420 \geq 37.16 x + 247.52} \][/tex]
