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

Question

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.

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

Answer 2

To solve this problem, let's go through the steps again to find the number of students who chose each color as their favorite.

Let's assume the number of students who liked purple is "x."

The problem states that twenty more students liked blue than purple. So, the number of students who liked blue would be "x + 20."

Similarly, it states that eight fewer students liked green than blue. So, the number of students who liked green would be "(x + 20) - 8," which can be simplified to "x + 12."

Now, let's add up the number of students who liked each color:

x (purple) + (x + 20) (blue) + (x + 12) (green) = 200

Combining like terms, we get:

3x + 32 = 200

Subtracting 32 from both sides:

3x = 168

Finally, dividing both sides by 3:

x = 56

So, the number of students who liked purple is 56.

To find the number of students who liked blue and green, we substitute this value back into our expressions:

Number of students who liked blue = x + 20 = 56 + 20 = 76
Number of students who liked green = x + 12 = 56 + 12 = 68

Therefore, there were 56 students who liked purple, 76 students who liked blue, and 68 students who liked green.