To determine the quantities of bags of popcorn ([tex]$x$[/tex]) and bottles of soda ([tex]$y$[/tex]) that should be purchased in order to receive a souvenir poster, we need to set up a linear inequality that represents the condition where the total cost exceeds [tex]$\$[/tex]60[tex]$.
1. Identify the cost of each item:
- A bag of popcorn costs \(\$[/tex]6\).
- A bottle of soda costs [tex]\(\$3.50\)[/tex].
2. Express the total cost:
- The total cost for [tex]$x$[/tex] bags of popcorn is [tex]\(6x\)[/tex].
- The total cost for [tex]$y$[/tex] bottles of soda is [tex]\(3.5y\)[/tex].
3. Combine the costs:
- The combined total cost for [tex]$x$[/tex] bags of popcorn and [tex]$y$[/tex] bottles of soda is [tex]\(6x + 3.5y\)[/tex].
4. Set up the inequality:
- In order to receive a souvenir poster, the total cost must exceed [tex]$\$[/tex]60[tex]$. However, to ensure customers are eligible for the poster even if they spend exactly \$[/tex]60, we represent this with the inequality [tex]\(6x + 3.5y \geq 60\)[/tex].
Therefore, the correct linear inequality that can be used is:
[tex]\[ 6x + 3.5y \geq 60 \][/tex]
This inequality ensures that the total expenditure on bags of popcorn and bottles of soda is at least \$60, making it possible for the customer to receive the souvenir poster.
