Question

Arturo has $480 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $201.87. He buys 3 bicycle reflectors for $9.82 each and a pair of bike gloves for $15.79 . He plans to spend some or all of the money he has left to buy new biking outfits for $32.80 each.

Answer 1

`\begin{gathered} 247.12+32.80x\le480 \\ 7\text{ outfits} \end{gathered}`

Step-by-step explanation

Arturo has $480 to spend.

He has spent:

=> $201.87 on a new bike

=> $9.82 on each of 3 bicycle reflectors

=> $15.79 on a pair of bike gloves

The total amount he has spent is:

`\begin{gathered} 201.87+(3\cdot9.82)+15.79 \\ \text{ \$}247.12 \end{gathered}`

He wants to buy new biking outfits for $32.80 each.

Let the number of outfits he can buy be x.

This means that the cost of x outfits is:

`\begin{gathered} 32.80\cdot x \\ \text{ \$32.80x} \end{gathered}`

The sum of the amount he has spent and the cost of the outfits must be less than or equal to the amount he has to spend.

This means that the inequality that represents the situation is:

`247.12+32.80x\le480`

To solve this, collect like terms and simplify:

`\begin{gathered} 32.80x\le480-247.12 \\ 32.80x\le232.88 \\ \Rightarrow x\le(232.88)/(32.8) \\ x\le7.1 \end{gathered}`

This means that Arturo can only buy 7 outfits while staying within his budget.