In a random sample of 200 students who were asked their favorite color, it was found that twenty more students liked blue than purple and eight fewer
liked green than blue.

a. Write equations that represent this information.

I had expected you to set
x + x+20 + x+12 = 200
3x = 200 - 20 - 12
3x = 168
x = 56

now back into my definitions:
purple --- 56
blue --- 56+20 = 76
green 56+12 = 68

check:
are 200 people accounted for ? YES
do 20 more people like blue than purple? YES
Do 8 fewer like green than blue ? YES

What are the options