Unit 2 Learning Checkpoint 2

Jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. If m represents the number of ounces of mango juice in the blend and p represents the number of ounces of papaya juice in the blend, which of the following inequalities represents this scenario?

• (2, 6)

• (1, 3)

• (2, 1)

• (4, -2)

KickIt Athletic Wear sells T-shirts for $25 each and sweatshirts for $40 each. The sales of T-shirts and sweatshirts are the only sources of revenue for KickIt, and the company needs to collect at least $10,000 in revenue per month to stay profitable. If the x-axis represents the number of T-shirts sold per month and the y-axis represents the number of sweatshirts sold per month, which of the following graphs represents the solution set for KickIt Athletic Wear to stay profitable each month?

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When Margo makes cheese ravioli, she uses both ricotta and mozzarella cheeses to make the filling. She often varies the proportions of the cheeses that she uses, but the number of ounces of ricotta cheese, r, is always more than 3 times the number of ounces of mozzarella cheese, m. For one batch of ravioli that Margo makes, she spends less than $8 on the cheeses. The ricotta cheese costs $0.24 per ounce, and the mozzarella cheese costs $0.15 per ounce. For which of the following systems of inequalities do the positive solutions represent all possible combinations of numbers of ounces of ricotta and mozzarella cheeses that Margo could have used for this batch?

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Which of the following graphs shows the solution set to the system of linear inequalities shown?

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Selena is the manager for the high school football team. She is responsible for organizing dinner for the team before the homecoming game. Selena is planning to get turkey sandwiches and servings of frozen yogurt for the team dinner. The coach wants the team dinner to provide each player with between 550 and 950 total calories and no more than 1,000 milligrams of sodium. The table shown gives the number of calories and milligrams of sodium per turkey sandwich and serving of frozen yogurt.

Selena creates a system of inequalities to determine possible combinations for the number of turkey sandwiches, t , and the number of servings of frozen yogurt, f, a player could eat and still remain within the coach’s calorie and sodium requirements. Which of the following systems represents this scenario, for t ≥ 0 and f ≥ 0 ?

The shaded region in the xy-plane shown is the graph of the solution to a system of two inequalities. Which of the following could be the system of inequalities?

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The graph of a system of linear inequalities in two variables is shown. Which of the following systems of inequalities is the algebraic representation of the graph?

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Which of the following statements provides sufficient reasoning as to why the ordered pair (-1, 2) is or is not a solution to the given system of inequalities?

• The ordered pair is a solution because it satisfies both inequalities.

• The ordered pair is a solution because it satisfies at least one of the inequalities.

• The ordered pair is not a solution because it satisfies only one of the inequalities.

• The ordered pair is not a solution because it does not satisfy either of the inequalities.