a+b = 146 -> a = 146-b
b+c = 100 -> c = 100-b
13a+3b+2c = 1582
13(146-b)+3b+2(100-b) = 1582
1898-13b+3b+200-2b = 1582
2098-12b = 1582
-12b = 1582-2098
-12b = -516 /*(-1)
12b = 516
b = 516/12
b = 43.
a = 146-b
a = 146-43
a = 103.
c = 100-b
c = 100-43
c = 57.
verificare : 13a+3b+2c = 13*103+3*43+2*57 = 1339+129+114 = 1339+243 = 1582. (adevarat)