Question

The ratio of rock music to total CDs that Ella owns is 25/40. Paolo has 50 rock music CDs. The ratio of rock music to total CDs in the collection is equal to the ratio of rock music to total CDs in Ella's collection. How many CDs do they own?

Answer 1

$\frac{25}{40} = \frac{50}{x}\\\\\ Cross\ multiply.\\\\25\times x=50\times40\\\\25x=2000\\\\ Divide\ by\ 25\ on\ both\ sides.\\\\x=80\\\\40+80={\boxed{120}$

Answer 2

They own a total of 120 CDs. Ella's CD is 40 while Paolo's CD is 80.

Given:
Ella's ratio of rock music to total CDs = 25/40
Paolo's ratio of rock music to total CDs = 50/x

25/40 = 50/x
25x = 40*50
25x = 2000
25x/25 = 2000/25
x = 80 

Total CDs
Ella           =   40
Paolo        =   80
Total CDs = 120