SOLUTION: Alpha has £160 more than beta. After giving1/10 of his money to Beta, Alpha has three times as much money as Beta. How much money do they each have to start with?

a = b + 160                 (1)

a - 0.1a = 3*(b + 0.1a)     (2)



Equation (2) is equivalent to

0.9a = 3b + 0.3a      or

0.9a - 0.3a = 3b,

0.6a = 3b                   (3)



From eq(1), substitute a = b+160 into eq(3).



0.6*(b+160) = 3b


0.6*b + 0.6*160 = 3b

0.6*160 = 3b - 0.6b

96           = 2.4*b


b            =  = 40.


ANSWER.  Beta started with £40;  Alpha started with  £40 + £160 = £200.


CHECK.   200 - 20 = 180;  40 + 20 = 60.   180 is three times 60.   ! Correct !