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

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