2a/3 = 5b/6 = 8c/9 = k
Atunci 2a = 3k, adica a = 3k/2
5b = 6k, adica b = 6k/5
8c = 9k, adica c = 9k/8
Dar a+b+c = 51, adica:
3k/2 + 6k/5 + 9k/8 = 51
60k/40 + 48k/40 + 45k/40 = 51
153k/40 = 51
153k = 40*51
k = 40*51/153 = 40*51/3*51 = 40/3
Revenim la sirul de rapoarte:
2a/3 = 40/3 => 2a = 40 => a = 20
5b/6 = 40/3 => 15b = 240 => b = 16
8c/9 = 40/3 => 24c = 360 => c = 15
