Question

the average height of students of a class is increased by 0.2 cm, if a student of height 172 cm is added to the class. If 2 students of average height 160 cm leaves the class, the average height increases by 0.8 cm. How many students are there in the class?​

Answer 1

Recall the following formula:

$\text{Average}=\frac{\text{Total sum of observations}}{\text{Number of observations}}$

Consider the original number of students = x

Sum of their height = y

Then,

$\text{Original average height}=\frac{y}{x}$

According to the question,

$\frac{y}{x}+0.2=\frac{y+172}{x+1}$

$\frac{y}{x}+0.8=\frac{y-320}{x-2}$

Using a graphing calculator,

The intersection point of these two curves is (21,3519.6)

Therefore, there would be 21 students in the class.