Question

Ranjana wants to distribute 540 oranges among students. 30 students were increased each will get 3 oranges less. Find no. Of students

Answer 1

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1

Secondary SchoolMath5 points

Ranjana wants to distribute 540 oranges among some students.if 30 students were more each would get 3 oranges less.find the number of student's.

Ask for details Follow Report by Danish1111510.05.2018

Answers



Kmg13teen Virtuoso

Let the number of students be x

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

By first condition

xy=540..................(1)
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By second condition,

(x+30)(y-3)=540

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

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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
10 y^2-30y = 540

Dividing each term by 10
y^2 - 3y = 54
Moving the constant to right

y^2 - 3y-54 = 0

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

y^2 +6y -9y -54 = 0
In first two terms, getting common as y and in next two getting common as 9

y(y±6) -9(y+6) = 0
Again common as (y+6)
(y-9) (y+6) = 0
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 



y = 9




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




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