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.
Find the number of students who chose each color as their favorite.
To solve this problem, we can set up an equation based on the given information.
Let's denote the number of students who liked purple as "x". Since twenty more students liked blue than purple, the number of students who liked blue is "x + 20".
Similarly, the number of students who liked green is "x + 20 - 8", which simplifies to "x + 12".
Now, we are given that the total number of students surveyed is 200. So we can set up the equation:
x + (x + 20) + (x + 12) = 200
Simplifying the equation:
3x + 32 = 200
Subtracting 32 from both sides:
3x = 168
Dividing both sides by 3:
x = 56
So, the number of students who liked purple is 56.
Plugging this value back into our equations, the number of students who liked blue is:
56 + 20 = 76
And the number of students who liked green is:
56 + 12 = 68
Therefore, there are 56 students who liked purple, 76 students who liked blue, and 68 students who liked green as their favorite color.