Let's let N = the total number of cookies shared.

We wish to divide a number N into 3 parts in the ratio of a:b:c, so the
parts are given by these formulas:

×N, ×N, and ×N

We wish to divide N cookies into 3 parts in the ratio of 4:5:1 

×N = ×N = ×N = Ali's share

×N = ×N = ×N = James' share

×N = ×N = Jason's share

Now we notice the words:

To get the equation we use this:

          =  + 45

           ×N = ×N + 45

Clear of fractions by multiplying all three terms by 10

        10××N = 10××N + 10×45
            4N = N + 450
            3N = 450
             N = 150 cookies shared

That's the answer.  To check it:

×150 = ×150 = ×150 = 60 = Ali's share

×150 = ×150 = ×150 = 75 = James' share

×150 = ×150 = 15 = Jason's share

The sum is 60 + 75 + 15 = 150  That part checks.

Ali received 60 cookies and Jason received 15 cookies, and indeed,
60 is 45 more than 15.

So the answer 150 is correct.

Edwin