Question

.Natalie has $680 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 $383.33.• She buys 2 bicycle reflectors for $7.61 each and a pair of bike gloves for $22.01.She plans to spend some or all of the money she has left to buy new biking outfitsfor $32.43 eachWrite and solve an inequality which can be used to determine x, the number ofoutfits Natalie can purchase while staying within her budget.< 1 >Inequality:Submit Answerattempt 1 out of

Answer 1

Answer:

Writing the inequality, we have;

$420.56+32.43x\leq680$

the solution to the inequality is;

$x\leq8$

Explanation:

Given that Natalie has $680 to spend at a bicycle store for some new gear and biking outfits.

Total spending must not exceed $680

$\text{total spending }\leq680$

She buys a new bicycle for $383.33.

• She buys 2 bicycle reflectors for $7.61 each and a pair of bike gloves for $22.01.

She plans to spend some or all of the money she has left to buy new biking outfits

for $32.43 each.

let x represent the number of biking outfits she can buy.

Total spending is;

$\begin{gathered} 383.33+2(7.61)+22.01+32.43(x) \\ 420.56+32.43x \end{gathered}$

Writing the inequality, we have;

$420.56+32.43x\leq680$

we can now solve the inequality;

$\begin{gathered} 420.56+32.43x\leq680 \\ \text{subtract 420.56 from both sides;} \\ 420.56-420.56+32.43x\leq680-420.56 \\ 32.43x\leq259.44 \\ \text{divide both sides by 32.43} \\ \frac{32.43x}{32.43}\leq\frac{259.44}{32.43} \\ x\leq8 \end{gathered}$

Therefore, the solution to the inequality is;

$x\leq8$