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 outfitsfor $51.03 each...Write and solve an inequality which can be used to determine x, the number ofoutfits Brianna can purchase while staying within her budget.Inequality:Submit Answerattempt 1 out of 3

Answer 1

Consider the expenses made by Brianna.

Bicycle for $261.04,

Three bicycle reflectors for $13.07, means $39.21,

A pair of bike gloves for $13.57,

Thus, the total expense till now,

`\text{Expense}=261.04+39.21+13.57=313.82`

Given that Brianna initially had $620, so the amount left after making the above expense is calculated as,

`\text{Amount Left=620-313.82=306.18}`

Given that she plans to spend all or some of this $306.18 to buy outfits which cost $51.03 each. If 'x' is the number of outfits purchased by Brianna then,

`51.03* x\leq306.18\Rightarrow x\leq(306.18)/(51.03)\Rightarrow x\leq6`

Thus, the required inequality for the number of outfiits 'x' is obtained, which has the solution region from negative infinity to 6 . But as we know that the number of outfits cannot be less than zero,

`x\ge0`

Combine both the results. It is observed that the solution region the values of 'x' which are less than 6 but not less than 0, therefore the solution is,

`0\leq x\leq6`

The corresponding diagram is given below,