Question

please help me and please don't scam​

Answer 1

[Ignore the italics part if you wanna make it to the end quick(Tho, its not much)]

Answer:

There are a total of 1400 students in the school.

Step-by-step explanation:

To solve this, let's take some unknown amount to be x.

This totally depends upon you, if you want you can take the number of students practicing soccer to be x or something else.

In general, the quantity asked to be discovered is taken as x.

In the question, we require to find out the number of students in the school!

So,

Let the number of students in the school be x,

Now, let's start collecting information

• 5/ 7 of the students like football

= 5x/ 7 students

• 3/ 5 of the students like cricket

= 3x/ 5 students

• 500 students like both

• 60 students like none

Comparing this information with Sets and Venn Diagram

If there are two sets A and B

$\boxed {\mathfrak { n(A \cup B) = n(A) + n(B) - n(A \cap B) }}$

(This is an important relation, the backbone of this problem.)

1. n(A∪B) => number of elements in the set of A union B
2. n(A) => number of elements in set A
3. n(B) => number of elements in set B
4. n(A∩B) => number of elements common in sets A and B

Now, let set A represent football loving students and set B represents cricket loving students.

Then,

• A∪B represents total number of students interested in these two sports 'as a whole'

• A∩B represents students interested in 'both' of these sports

(Note how the emphasis is laid on the underlined words)

Therefore, n(A∪B) =  total students in school - those not interested in these sports

• n(A∪B) = x - 60

• n(A) = 5x/ 7

• n(B) = 3x/ 5

n(A∩B) = students interested in both the sports

• n(A∩B) = 500

$\boxed {\mathfrak { n(A \cup B) = n(A) + n(B) - n(A \cap B) }}$

x - 60 = 5x/ 7 + 3x/ 5 - 500

• combining like terms

500 - 60 = 5x/ 7 + 3x/ 5 - x

440 = ( 25x + 21x - 35x)/ 35

440 = 11x/ 35

x = (440 × 35)/ 11

x = 40 × 35

x = 1400

and since x was the total number of students in the school,

The number of students in school is 1400.

[The attachment will help you visualize it better]

                               

Hope this helps!