Nevaeh has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $383.32. She buys 4 bicycle reflectors for $9.09 each and a pair of bike gloves for $21.07. She plans to spend some or all of the money she has left to buy new biking outfits for $39.75 each.

Given - Nevaeh has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $383.32. She buys 4 bicycle reflectors for $9.09 each and a pair of bike gloves for $21.07. She plans to spend some or all of the money she has left to buy new biking outfits for $39.75 each.

To find - Write and solve an inequality which can be used to determine x where x, the number of outfits Nevaeh can purchase while staying within her budget.

Proof -

Given that,

Total money Nevaeh have = $ 560

She spent money on bicycle = $ 383.32

She spend money on 1 reflector = $ 9.09

As she buy 4 bicycle reflector, So

Total money spent on bicycle reflector = $ 4×9.09 = $ 36.36

She spend money on a pair of bike gloves = $ 21.07

So,

Total money she spend on the items = $ 383.32 + 36.36 + 21.07

= $ 440.75

⇒Total money she spend on the items = $ 440.75

So,

Total money Left = $ 560 - $ 440.75 = $ 119.25

Now,

She plans to spend some or all of the money she has left to buy new biking outfits for $ 39.75 each.

Let us assume ,

The number of outfits she purchase with the left money = x

AS,

each outfit cost = $ 39.75

So, x outfits cost = $ 39.75 x

Now,

$ 39.75 x = $ 119.25 (because total money left = $ 119.25)

⇒ x = [tex]\frac{119.25}{39.75}[/tex] = 3

∴ we get

The number of outfits she purchase with the left money = x = 3