The students in a political science class are divided up into three categories: liberal,
conservative, or moderate. There are five more conservatives than moderates, and twice as
many liberals as conservatives. How many of each type are there if there is a total of 87
students in the class?
just put the words into symbols. If the numbers are x,y,z, respectively, then we are told that
y=z+5
x=2y
x+y+z=87
Now just solve the equations.
Let m represent the moderates.
m + m + 5 + 2(m + 5) = 87
4m + 15 = 87
4m = 72
m = 18
To solve this problem, we can use a system of equations.
Let's assign variables to represent the number of students in each category:
Let C represent the number of conservatives,
Let M represent the number of moderates, and
Let L represent the number of liberals.
According to the problem, we have three pieces of information:
1. "There are five more conservatives than moderates" -> C = M + 5
2. "Twice as many liberals as conservatives" -> L = 2C
3. "There is a total of 87 students in the class" -> C + M + L = 87
Now, we can use these equations to find the values of C, M, and L.
First, we'll substitute C = M + 5 from equation 1 into equation 3:
(M + 5) + M + L = 87
Next, we substitute L = 2C from equation 2 into the previous equation:
(M + 5) + M + 2(M + 5) = 87
Now, we simplify and solve for M:
M + 5 + M + 2M + 10 = 87
4M + 15 = 87
4M = 72
M = 18
Substituting the value of M back into C = M + 5:
C = 18 + 5 = 23
And substituting C = 23 into L = 2C:
L = 2 * 23 = 46
So, there are 23 conservatives, 18 moderates, and 46 liberals in the class.