Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
For Tom's collection, the number of CDs after "x" months can be represented by the equation:
y = 30 + 1x
For Nita's collection, the number of CDs after "x" months can be represented by the equation:
y = 18 + 5x
To find the number of months after which they will have the same number of CDs, we set the two equations equal to each other and solve for "x":
30 + 1x = 18 + 5x
Subtracting 1x and 18 from both sides:
30 - 18 = 5x - 1x
12 = 4x
Dividing both sides by 4:
12/4 = 4x/4
3 = x
Therefore, after 3 months, Tom and Nita will have the same number of CDs.