Question 1105659

Bob starts with B dollars:  (4/7)B = k    (1)    (Bob spent 3/7 so he has 4/7 left…)
John starts with J dollars:   (4/5)J = k   (2)
Alan starts with A dollars:   (2/3)A = k   (3)

(3/7)B + (1/5)J + (1/3)A = 144   (4)

From (1) and (2):  (4/7)B = k = (4/5)J —>   J = (5/7)B
From (1) and (3): (4/7)B = k = (2/3)A —>   A = (6/7)B

Now substitute these last two equations for J and A in (4) to get one equation in one unknown:

        (3/7)B + (1/5)(5/7)B + (1/3)(6/7)B = 144
        (3/7)B + (1/7)B + (2/7)B = 144
           (6/7)B = 144
                   B = 144*7 / 6 = 168  —> A = 144,  J = 120

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 Ans:  Bob started with  $168,  Alan with $144, and John with $120
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Check:   
                  (3/7)(168) + (1/5)(120) + (1/3)(144)
             =   72  + 24 + 48
             =   144  (ok)