Question

A store sells notepads in packages of 24 and packages of 6. The organizers of a conference need to prepare at least 200 notepads for the event. Write an inequality to represent the situation, graph it, and then name two possible combinations of large and small packages of notepads that will meet the number of notepads needed for the event.

A) Inequality: 24x + 6y ≥ 200; Combinations: (8, 8) and (6, 10)
B) Inequality: 6x + 24y ≥ 200; Combinations: (10, 6) and (8, 8)
C) Inequality: 24x + 6y ≤ 200; Combinations: (8, 8) and (10, 6)
D) Inequality: 6x + 24y ≤ 200; Combinations: (6, 10) and (8, 8)

Answer 1

The correct inequality is 24x + 6y ≥ 200, representing the number of large and small notepad packages needed. Two possible combinations that meet the requirement are (8, 8) and (6, 10).

Step-by-step explanation:

The correct answer is A) Inequality: 24x + 6y ≥ 200; Combinations: (8, 8) and (6, 10). This represents the scenario wherein 'x' is the number of large packages (24 notepads each) and 'y' is the number of small packages (6 notepads each). The inequality shows that the total number of notepads from the packages must be at least 200 for the conference.

To find suitable combinations, you substitute different values of 'x' and 'y' into the inequality to find solutions that satisfy it. For example, with (8, 8) we have 24(8) + 6(8) = 192 + 48 = 240 which is greater than 200. Likewise, for (6, 10) we have 24(6) + 6(10) = 144 + 60 = 204, which also fulfills the requirement.