The ratio of rock music total cds that ella owns is 25/40 .paolo has 59 rock music cds. the ratio of rock music to total cds in his collections is equivalent to the ratio of rock music to total cds in ella's collection .how many cds do they own?

So, the given information tells us that the ratios between ella's rock music to total cds and paolo's rock music to total cds is the same.  This means that we can set them up in a proportion equal to each other. (Let x represent the amount of total cds in paolo's collection)

25/40=59/x

Next, to simplify this equation, we need to use cross-products to cancel out the fraction bars.

25   59
     =
40    x

If done correctly, the resulting equation is 20*x=59*40

When simplified, the resulting equation is 20x=2360

Finally, we need to divide both sides by 20, in order to find out what integer represents x in this equation.

x=118

This means that Paolo has a total of 118 cds in his collection.
 
The question asks how many CDs Paolo and Ella own together.  To figure this out, all you need to do is add how many CDs Ella has (40) to how many CDs Paolo has (118).

40+118=158.

Paolo and Ella's combined collection of total CDs is 158 CDS.