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 find the number of students who chose each color as their favorite, we can use algebraic equations to represent the given information.
Let's assume the number of students who liked purple is x.
Then, the number of students who liked blue would be x + 20 (as 20 more students liked blue than purple).
And the number of students who liked green would be (x + 20) - 8 (as 8 fewer liked green than blue).
According to the problem, the sum of the number of students who liked each color should be equal to the total sample size (200).
So, we can write the equation as:
x + x + 20 + (x + 20) - 8 = 200
Now, let's solve the equation to find the value of x, which represents the number of students who liked purple.
Combining like terms:
3x + 32 = 200
Subtracting 32 from both sides of the equation:
3x = 168
Dividing both sides by 3:
x = 56
Therefore, 56 students chose purple as their favorite color.
The number of students who chose blue would be x + 20 = 56 + 20 = 76.
The number of students who chose green would be (x + 20) - 8 = 56 + 20 - 8 = 68.
So, the final answer is:
Purple: 56 students
Blue: 76 students
Green: 68 students