Question

Ranjana wants to distribute 540 oranges among some students . if 30 students were more each would get 3 oranges less .find the no.of students​

Answer 1

Answer:

Step-by-step explanation:

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Let the number of students be x

and the number of oranges distributed per one student be y.

By first condition

xy=540..................(1)________________________________________________

By second condition,

(x+30)(y-3)=540But from (1), 540 = xy

thus

(x+30)(y-3)=xy

Multiply on the L.H.S

x(y-3)+30(y-3)=xy

xy-3x+30y-90= xy

Subtracting xy from both sides,

-3x+30y-90=0

Dividing each term by 3

-x+10y-30=0. (Anything divides 0 becomes zero)

-x-30= -10y. ( Moving 10y to R.H.S. Yeah it's sign

changes)

-1(x+30)= -1(10y). ( Making -1 as common on both sides)

x+30= 10y. ( Say Multiplying by -1 on both sides)

------------------x=10y-30. (Moving 30 to R.H.S and got value of

x)_______________________________________________

Let's substitute value of x in equation (1) ( Hope you didn't forgot equation (1) that was above)

Equation (1) was

xy = 540

(10y-30)(y)=540

Now, I have to change keyboard.

Multiplying the terms

Dividing each term by 10

Moving the constant to right

Oh! It's a quadratic equation, there are various ways to solve it

Let us go for the beginners method i.e "FACTORISATION"

SPLITING -3y as a sum or difference

In first two terms, getting common as y and in next two getting common as 9

Again common as (y+6)

Now

y-9 = 0. or. y+6 = 0

y = 9. or. y = -6

These are the roots of the quadratic equation

Let's confirm which one is useful to us

y means the number of oranges distributed per one. So it is not going to be negative

So

is the required solution

OH BUT WE WANT THE NUMBER OF STUDENTS

From (1)

xy=540

x(9)=540

x=540/9

x=60

ANS:- THE NUMBER OF STUDENTS IS 60