Question

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. Find the number of months after which they will have the same number of CDs. Show your work.

Answer 1

30 + 1x = 18 + 5x
subtract 18 from both sides
30 - 18 + 1x = 18 - 18 + 5x
12 + 1x = 5x
subtract 1x from both sides
12 + 1x - 1x = 5x - 1x
12 = 4x
To clear the multiplication by 4, divide both sides by 4
12/4 = 4x/4
3 = x
It will take 3 months until they have the same amount of CD's
They will each have 33 CD's