Question

6. Astore sella notepads in packages of 24 and packages of 6. The organizerof a conference needs to prepare at least 200 notepads for the event.6a. Would they have enough notepads if they bought seven packages of 24 pmand one package of 6?Your answer6b. Would they have enough notepads if they bought five packages of 24and fitteen packages of 6?Your answer6c. Write an inequality to represent the relationship between the number of large and small packages of notepads and the number of notepads needed for event.6d. Use graphing technology to graph the solution set to the inequality. Then, use the graph to name two other possible combinations of large and small packages of notepads that will meet the number of notepads needed for the event.

Answer 1

The organizers need to prepare 200 notepads for the event.

a. If they bought 7 packages of 24 and 1 package of 6. The total notepad will be :

`7(24)+1(6)=174`

Which is NOT enough with the required number of notepads.

b. If they bought 5 packages of 24 and 15 packages of 6. The total notepad will be :

`5(24)+15(6)=210`

Which is enough with the required number of notepads.

c. Let x = number of packages of 24 and y = number of packages of 6.

The sum must be atleast 200 which is the requirement for the event

The inequality will be :

`24x+6y\ge200`

d. Using desmos, the graph will be :

The other solutions will be in the region and the other possible combinations are :

(5, 20) and (10, 10)

5 packages of 24 and 20 packages of 6

10 packages of 24 and 10 packages of 6