Avery has $760 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 $239.70. She buys 3 bicycle reflectors for $18.63 each and a pair of bike gloves for $30.79. She plans to spend some or all of the money she has left to buy new biking outfits for $78.84 each. Write and solve an inequality which can be used to determine xx, the number of outfits Avery can purchase while staying within her budget.

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MrRoyal MrRoyal · Answer 1 · 2020-12-13T07:13:18+01:00

Answer:

Not more than 5 outfits

Step-by-step explanation:

Given

[tex]Total = \$760[/tex]

[tex]New\ Bicycle = \$239.70[/tex]

[tex]Reflector (3) = \$18.63[/tex] (each)

[tex]Glove = \$30.79[/tex]

First, we calculate the amount left.

[tex]Amount = Total - (New\ Bicycle + Reflector * 3 + Glove)[/tex]

[tex]Amount = \$760 - (\$239.70 + \$18.63 * 3 + \$30.79)[/tex]

[tex]Amount = \$760 - (\$239.70 + \$55.89 + \$30.79)[/tex]

[tex]Amount = \$760 - (\$326.38)[/tex]

[tex]Amount = \$760 - \$326.38[/tex]

[tex]Amount = \$433.62[/tex]

An outfit costs $78.84 and he plans to buy x outfits.

The inequality is represented as follows:

[tex]\$78.84 * x \leq \$433.62[/tex]

i.e. the amount to spend on outfits can't exceed $433.62

Divide both sides by $78.84

[tex]\frac{\$78.84 * x}{\$78.84} \leq \frac{\$433.62}{\$78.84}[/tex]

[tex]x \leq \frac{\$433.62}{\$78.84}[/tex]

[tex]x \leq \frac{433.62}{78.84}[/tex]

[tex]x \leq 5.5[/tex]

Since there is no 0.5 outfit, then She can only afford a maximum of 5 outfits to stay within budget.