Greenestamps did it the most elementary way. Think I'll do it using
matrices.  Maybe you've gotten that far.

>>>Ali, Ben, Cain and Dan, shared a sum of money.

>>>Let A,B.C.D be the fractions of their shares.  Then the sum of the
four fractions must be 1 (whole).

So 

>>>Ali has 1/2 of the total amount of money that Ben, Cain and Dan have.



>>>Ben has 1/3 of the total amount of money that Ali, Cain and Dan have.



>>>Cain has 1/7 of the total amount of money that Ali, Ben and Dan have.



The system is



The matrix is



Do row operations on that to get the row reduced echelon form (RREF)
of the matrix above.  Your TI-84 can handle that if you understand the
matrix feature.

The RREF matrix form of that is as below



So Ali got 1/3, Ben got 1/4, Cain got 1/8, and Dan got 1/7.

------------------------------------

For (b)

Let $S = the total amount,

Then Dan's share was 7/24 of $S

So 
   
    

[Greenestamps was right!]]

Ali got 1/3 of $288 or $96
Ben got 1/4 of $288 or $72
Cain got 1/8 of $588 or $36
Dan got $84

Check:
The sum was $96
            $72
            $36
            $84
            ---
           $288 as we expected.  

Edwin