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

Noah manages a buffet at a local restaurant. He charges $10 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 $1 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 $130 per hour.

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

Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 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.

To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.

Type the correct answer in each box. Use numerals instead of words.

___ x2 + x + ___ ≥

Which possible buffet prices could Noah could charge and still maintain the restaurant owner’s revenue requirements?

Select the correct prices in the table.

$12 $13 $14 $15

Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.