65% students do algebra 35% do geometry 30 students do both 15% do neither What is the total number of students?

Question

65% students do algebra
35% do geometry
30 students do both
15% do neither
What is the total number of students?

Answer 1

we assume the total number of students is x

15% students do neither, that means 85% students do the algebra,  geometry, or do both.

 

85% x= 65% x + 35% x - 30

 

0.85 x = x - 30

 

0.15 x = 30

       

       x = 200

the total number of students is 200

Answer 2

Using the rules of sets and probability,

the total number of people can be determined by summing those who do algebra, those who do geometry, subtract those who do both (not to double count), and add those who do neither. So the total people are X, we have

.65x+.35x-30+.15x=x 

so solving

.15x=30

x=200

this checks out. 

Answer 3

Hi Sarika

 

You asked this question and it was answered, you can see from this link

 

https://www.wyzant.com/resources/answers/232405/65_students_do_algebra_35_do_geometry_30_students_do_both_15_do_neither_what_is_the_total_number_of_students