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.
like purple ---- x
liked blue ----- x+20
liked green ---- x+20 - 8 = x+12
what is
x + x+20 + x+12 ??
so, that would be 10.66666666666 then for x
or would it be 3x+12?
To find the number of students who chose each color as their favorite, we'll need to break the problem down and solve step by step. Let's assign variables to represent the number of students who liked each color:
Let:
P = number of students who liked purple
B = number of students who liked blue
G = number of students who liked green
According to the information given, we know the following:
1. "Twenty more students liked blue than purple": B = P + 20
2. "Eight fewer liked green than blue": G = B - 8
We can use these equations to solve for the variables and find the number of students who chose each color as their favorite.
Step 1: Start with the first equation: B = P + 20.
Step 2: Substitute B from the first equation into the second equation: G = (P + 20) - 8.
Simplify the equation: G = P + 12.
Step 3: We have two equations now: B = P + 20 and G = P + 12.
We can substitute the second equation into the first equation to eliminate P:
(P + 20) = (P + 12) + 20.
Simplify the equation: P + 20 = P + 32.
Step 4: Subtract P from both sides to get the solution: 20 = 32.
This is a contradiction, which suggests that there is no solution to the problem. It seems that there is an inconsistency or error in the given information.
To find the number of students who chose each color as their favorite, we need additional information or clarification regarding the problem.