Question

A minus B equals 25 A : b is equivalent 13:8

Answer 1

So, this includes some good old algebra. 
A minus B equals 25 A : b is equivalent 13:8

So, we have a couple things to write out. 
The ratio of a to b (a:b) is 13:8 
---> this means that 13a = 8b
I would solve for one of the variables. b seems a little bit easier, I guess so I'll solve for that one. 

(13/8)a=b
Therefore:
a-b=25
a-(13/8)a=25
(8/8)a-(13/8)a=25
-(5/8)a=25
-a=25 / (5/8)
-a = 25 * (8/5)
a= -40

Now, it probably wants both a and b solved. So to find b we just substitute in the value for a. Or, more easily, just solve the original equation with a substituted.
a-b=25
-40-b=25
-b=25+40
-b=-65
b=-65

and to check:

13a = 8b
13(-40)=8(-65)
-520=-520
 
and 
a-b=?
-40-(-65)=25