In a random sample of 200 students who were asked their favorite color, it was found

Question

that twenty more students liked blue than purple and eight fewer liked green than blue.
Find the number of students who chose each color as their favorite.

I posted this question earlier and what the tutor said confused me.....

I got to

like purple ---- x
liked blue ----- x+20
liked green ---- x+20 - 8 = x+12

x + x+20 + x+12

But then when I tried to solve for x it came out as a decimal....10.66666666666666667
I feel like the answer would be a whole number because they're asking for how many STUDENTS and students shouldn't be a fraction right?

Answer 1

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

My answer is correct