the average age of a group of teachers and student is 20. the average age of the teachers is 35. the average age of the students is 15. what is the ratio number of teacher to number of students ?
Let x be the number of students and y be the number of teachers. You want to know y/x.
The sum of the products of people and there ages can be written as
(x + y)*20 or 15 x + 35 y.
Therefore
(x + y)*20 = 15 x + 35 y
5x = 15 y.
y/x = 1/3 is the teacher/student ratio.
To find the ratio of the number of teachers to the number of students, we need to calculate the individual numbers first. Let's use algebra to solve it step by step:
Let's assume the number of teachers is x, and the number of students is y.
Given:
The average age of the teachers = 35
The average age of the students = 15
The average age of the entire group = 20
According to the average formula,
Total age of the teachers = 35 * x
Total age of the students = 15 * y
Total age of the entire group = 20 * (x + y)
However, we also know that the average age of the entire group is 20, so we can create an equation:
(35 * x + 15 * y) / (x + y) = 20
Now, we can solve this equation to find the values of x and y.
First, let's solve the equation for y:
35 * x + 15 * y = 20 * (x + y)
35x + 15y = 20x + 20y
15x - 20y = 0
3x - 4y = 0 ---- (equation 1)
Now, let's solve the equation for x:
35 * x + 15 * y = 20 * (x + y)
35x + 15y = 20x + 20y
15x - 5y = 0
3x - y = 0 ---- (equation 2)
Now, we have two equations:
Equation 1: 3x - 4y = 0
Equation 2: 3x - y = 0
We can solve these equations simultaneously using substitution or elimination method.
Let's solve it using the elimination method:
Multiply equation 2 by 4 and equation 1 by 1 to make the coefficients of 'x' equal:
4 * (3x - y) = 4 * 0
12x - 4y = 0 ---- (equation 3)
1 * (3x - 4y) = 1 * 0
3x - 4y = 0 ---- (equation 1)
Now, subtract equation 3 from equation 1:
(12x - 4y) - (3x - 4y) = 0 - 0
9x = 0
x = 0
Substituting x = 0 into equation 2:
3(0) - y = 0
-y = 0
y = 0
Since x = 0 and y = 0, it means there are no teachers or students in the group.
Therefore, the ratio of the number of teachers to the number of students is 0:0.