The number of comedy DVDs a store receives can be represented by the function 7w + 2, where the w represents the number of weeks. The number of drama DVDs the same store receives is show in the table. How may new comedy DVDs and drama DVDs will the store have in week 6? Weeks are 1,2,3 / Number of Drama DVDs are 3,6,9

The store will have 44 comedy DVDs and 18 drama DVDs

Step-by-step explanation:

The number of drama DVDs the same store receives is show in the table

Weeks : 1 : 2 : 3

DVDs : 3 : 6 : 9

Let us make the function that represents the table

The rate of change of the number of the DVDs to the number of the week is constant, then the relation between them is linear

∵ The number of weeks is w

∵ The rate of change of the number of DVDs = (6-3) / (2-1) = 3/1 = 3

- The function will be equal 3 times the number of weeks

∴ The number of drama DVDs = 3 w

∵ w = 6

∴ The number of drama DVDs = 3 (6) = 18

∵ The function 7 w + 2 represents the number of comedy DVDs

∴ The number of comedy DVDs = 7 w + 2

∵ w = 6

∴ The number of comedy DVDs = 7 (6) + 2 = 42 + 2

∴ The number of comedy DVDs = 44

The store will have 44 comedy DVDs and 18 drama DVDs