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Omar has [tex]\$660[/tex] 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 [tex]\$330.64[/tex].
- He buys 2 bicycle reflectors for [tex]\$15.34[/tex] each and a pair of bike gloves for [tex]\$34.47[/tex].
- He plans to spend some or all of the money he has left to buy new biking outfits for [tex]\$36.30[/tex] each.

Which inequality can be used to determine [tex]x[/tex], the maximum number of outfits Omar can purchase while staying within his budget?

A. [tex]660 \geq 36.3x + 395.79[/tex]

B. [tex]36.3 + 395.79x \leq 660[/tex]

C. [tex]36.3 + 395.79x \geq 660[/tex]

D. [tex]660 \leq 36.3x + 395.79[/tex]

Answer :

Let's break down the problem step-by-step to find the inequality that determines the maximum number of biking outfits Omar can purchase while staying within his budget of [tex]$660.

1. Calculate the total amount Omar has spent already:
- Cost of the new bicycle: $[/tex]330.64
- Cost of 2 bicycle reflectors: [tex]$15.34 each
\( \text{Total for reflectors} = 2 \times 15.34 = 30.68 \)
- Cost of the bike gloves: $[/tex]34.47

Adding these amounts together:
[tex]\( 330.64 + 30.68 + 34.47 \)[/tex]

Let's add these amounts step-by-step:
- First, add the cost of the bicycle and reflectors:
[tex]\( 330.64 + 30.68 = 361.32 \)[/tex]
- Then, add the cost of the gloves:
[tex]\( 361.32 + 34.47 = 395.79 \)[/tex]

Hence, the total amount spent so far is [tex]$395.79.

2. Calculate the remaining budget:
- Omar's total budget: $[/tex]660
- Total spent so far: [tex]$395.79

The amount left to spend is:
\( 660 - 395.79 = 264.21 \)

3. Set up the inequality for the number of outfits (where \( x \) is the number of outfits):
- The cost of each biking outfit: $[/tex]36.30

Let [tex]\( x \)[/tex] represent the number of outfits Omar can buy. The total cost for [tex]\( x \)[/tex] outfits would be:
[tex]\( 36.30 \times x \)[/tex]

To stay within the budget, the total spent plus the cost for [tex]\( x \)[/tex] outfits must be less than or equal to $660:
[tex]\( 395.79 + 36.30x \leq 660 \)[/tex]

Rewriting this inequality with the total budget on one side, we get:
[tex]\( 660 \geq 36.30x + 395.79 \)[/tex]

Therefore, the inequality that can be used to determine [tex]\( x \)[/tex], the maximum number of outfits Omar can purchase while staying within his budget, is:

[tex]\[ 660 \geq 36.3x + 395.79 \][/tex]

This corresponds to the given option:
[tex]\[ \boxed{660 \geq 36.3x + 395.79} \][/tex]

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Rewritten by : Barada