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(a) If box Y had 12u marbles at first, box X had ( 80 + 12u ) marbles.

After moving 1/4 from X to Y, X had 3(80 +12u)/4 =  ( 60 + 9u) marbles and box Y had (12u + 20 + 3u) = (15u + 20) marbles.

After moving 2/5 from Y to X, Y  had 3(15u+20)/5 = (9u + 12) marbles and box X had ( 60 + 9u + 6u + 8) = (68 + 15u) marbles.

Finally Box X had (68 + 15u + 53) = (121 + 15u) marbles

Given         121 + 15u = 2 (9u + 12)

121 + 15u = 18u + 24

3u = 97

u = 97/3

6u + 8 = 194 + 8 = 202

202  marbles were moved from Y to X.

(b) 9u + 12 = 9 ( 97/3) + 12 = 291 + 12 = 303

303 marbles were in Box Y in the end.

 

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