Question 536470
<pre>
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:

{{{a/(a+b+c)}}}×N, {{{b/(a+b+c)}}}×N, and {{{c/(a+b+c)}}}×N

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

{{{4/(4+5+1)}}}×N = {{{4/10}}}×N = {{{2/5}}}×N = Ali's share

{{{5/(4+5+1)}}}×N = {{{5/10}}}×N = {{{1/2}}}×N = James' share

{{{1/(4+5+1)}}}×N = {{{1/10}}}×N = Jason's share

Now we notice the words:
</pre>>>...Ali received 45 cookies more than Jason...<<<pre>

To get the equation we use this:

         {{{(matrix(2,1,    "Ali's", share))}}} = {{{(matrix(2,1,    "Jason's", share))}}} + 45

           {{{2/5}}}×N = {{{1/10}}}×N + 45

Clear of fractions by multiplying all three terms by 10

        10×{{{2/5}}}×N = 10×{{{1/10}}}×N + 10×45
            4N = N + 450
            3N = 450
             N = 150 cookies shared

That's the answer.  To check it:

{{{4/(4+5+1)}}}×150 = {{{4/10}}}×150 = {{{2/5}}}×150 = 60 = Ali's share

{{{5/(4+5+1)}}}×150 = {{{5/10}}}×150 = {{{1/2}}}×150 = 75 = James' share

{{{1/(4+5+1)}}}×150 = {{{1/10}}}×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</pre>