let

g = the number of green marbles, g>0, g is integer

p = the number of purple marbles, p>0, p is integer

a bag has green and purple marbles in a ratio of 2.5:

g : p = 2 : 5 cross-multiply

5g = 2p

there are 133 marbles in all:

g + p = 33

by solving the system of equations:

5g = 2p

g + p = 33

we find the system has not integer solutions

g = 9.4

p = 23.5

click here to see the step by step solution of the system of equations:

the system has no integer solutions thus this problem has no solutions.