In this activity, you will create quadratic inequalities in one variable and use them to solve problems. Read the scenario below, and then use the information to answer the questions that follow.

Noah manages a buffet at a local restaurant. He charges [tex]$\$[/tex] 10[tex]$ for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $[/tex]\[tex]$ 1$[/tex] increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of [tex]$\$[/tex] 130[tex]$ per hour.

Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.

\ \textless \ strong\ \textgreater \ Part A\ \textless \ /strong\ \textgreater \

Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that $[/tex]x[tex]$ represents the number of $[/tex]\[tex]$ 1$[/tex] increases in the cost of the buffet.

Enter the correct answer in the box. Type the cost expression on the first line and the customer expression on the second line.

Cost: \_\_\_\_

Customers: \_\_\_\_

To model the situation described, let's denote [tex]$ x $[/tex] as the number of \[tex]$1 increases in the cost of the buffet. ### Part A Expression for the cost per customer: Initially, the cost of the buffet is \$[/tex]10. For each \[tex]$1 increase, represented by $ x $, the cost increases by \$[/tex]1.

So, the cost per customer after [tex]$ x $[/tex] increases is:
[tex]\[ \text{Cost} = 10 + x \][/tex]

Expression for the average number of customers:
Initially, the average number of customers is 16. For every \$1 increase, represented by [tex]$ x $[/tex], the number of customers decreases by 2.

So, the average number of customers after [tex]$ x $[/tex] increases is:
[tex]\[ \text{Customers} = 16 - 2x \][/tex]

Thus, we have the following expressions:
[tex]\[ \boxed{10 + x} \][/tex]
[tex]\[ \boxed{16 - 2x} \][/tex]