A.2.22 Practice Problems

To qualify for a loan from a bank, the total in someone’s checking and savings accounts together must be $500 or more. a. Which of these inequalities best represents this situation?

b. Complete the graph so that it represents solutions to an inequality representing this situation.

The soccer team is selling bags of popcorn for $3 each and cups of lemonade for $2 each. To make a profit, they must collect a total of more than $120. a. Write an inequality to represent the number of bags of popcorn sold, p, and the number of cups of lemonade sold, c, in order to make a profit.

c. Explain how we could check if the boundary is included or excluded from the solution region.

Tickets to the aquarium are $11 for adults and $6 for children. An after-school program has a budget of $200 for a trip to the aquarium.                 If the boundary line in each graph represents the equation 11x + 6y = 200, which graph represents the cost constraint in this situation?

Tyler filled a small jar with quarters and dimes and donated it to his school's charity club. The club member receiving the jar asked, "Do you happen to know how much is in the jar?" Tyler said, "I know it's at least $8.50, but I don't know the exact amount." a. Write an inequality to represent the relationship between the number of dimes, d, the number of quarters, q, and the dollar amount of the money in the jar.

b. Graph the solution set to the inequality and explain what a solution means in this situation.

c. Suppose Tyler knew there are 25 dimes in the jar. Write an inequality that represents how many quarters could be in the jar.

Here is a graph of the equation 6x + 2y = -8. a. Are the points (1.5, -4) and (0, -4) solutions to the equation? Explain or show how you know.

b. Check if each of these points is a solution to the inequality 6x + 2y < -8: i. (-2, 2) ii. (4, -2) iii. (0, 0) iv. (-4, -4)

c. Are the points on the line included in the solution region? Explain how you know.