Four pupils

Four pupils divided $ 1485 so that the second received 50% less than the first, the third 1/2 less than a fourth and fourth $ 154 less than the first. How much money had each of them?

Correct result:

a =  572 $
b =  286 $
c =  209 $
d =  418 $

Solution:

a+b+c+d=1485 \ \\ b=a(1-50/100) = 0.5 a \ \\ c = d \cdot (1-1/2) = 0.5 d \ \\ d= a - 154 \ \\ \ \\ a + 0.5 a + 0.5(a-154) + a-154 = 1485 \ \\ \ \\ a = \dfrac{ 1485+154+0.5\cdot 154}{ 2+ 0.5 + 0.5} \ \\ \ \\ a=572 \ $
b= 286 \ $
c= 209 \ $
d= 418 \ $

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