Question

Brianna has $620 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 $261.04.
She buys 3 bicycle reflectors for $13.07 each and a pair of bike gloves for $13.57.
She plans to spend some or all of the money she has left to buy new biking outfits for $51.03 each.

Write and solve an inequality which can be used to determine xx, the number of outfits Brianna can purchase while staying within her budget.

Answer 1

Answer: 6 outfits

Explanation:

$620 should be greater than the price of the new bicycle + 3 * bicycle reflectors + a pair of bike gloves + unknown number of biking outfits

Therefore, the inequality will be:

620 ≥ 261.04 + 3 × 13.07 + 13.57 + 51.03x

620 ≥ 313.82 + 51.03x

`\text{Solving \ for \ x}`

`620\ge \:313.82+51.03x`

`\mathrm{Switch\:sides}`

`313.82+51.03x\le \:620`

`\mathrm{Multiply\:both\:sides\:by\:}100`

`313.82\cdot \:100+51.03x\cdot \:100\le \:620\cdot \:100`

`\mathrm{Refine}`

`31382+5103x\le \:62000`

`\mathrm{Subtract\:}31382\mathrm{\:from\:both\:sides}`

`31382+5103x-31382\le \:62000-31382`

`\mathrm{Simplify}`

`5103x\le \:30618`

`\mathrm{Divide\:both\:sides\:by\:}5103`

`(5103x)/(5103)\le (30618)/(5103)`

`\text{Simplify}`

`{x\le \:6}`

Therefore, Brianna can buy 6 or fewer outfits while staying within her budget