Пусть a,b,c -- искомые числа.
Тогда
a + b + c = 315
a = 7b/12
c = 2 1/6 b
7b/12 + b + 2 1/6 b = 315
7b/12 + b + 13b/6 = 315
7b/12 + 12b/12 + 26b/12 = 315
45b/12 = 315
15b/4 = 315
15b = 1260
b = 1260 : 15 = 84
a = 7b/12 = 7*84/12 = 49
с = 13b/6 = 13*84/6 = 182
Ответ: 49; 84; 182.