Existen tres órdenes de producción en proceso. las ordenes a y b juntas tienen 150 unidades; b y c juntas, 100 unidades, y a y c juntas, 150 unidades. ¿cuánto tiene cada orden?

Orders are a, b, c, lets write equations to represent the problem's info:
a + b = 150
b + c = 100
a + c = 150
so we have 3 unknowns and 3 equations, so we can solve.
Use the first equation:
a + b = 150
a = 150 - b
and substitute in the 3rd:
a + c = 150
150 - b + c = 150
then
b = c
and we can substitute that in the original equation:
b + c = 100
2b = 100
b = 50
c = 50
and substitute in the first equation:
a + b = 150
a = 150 - b = 150 - 50
a = 100
then a = 100, b = c = 50

Where’s the problems ? ?