Question

6400 notebooks were distributed among some
children. Had there been 80 children less, each
would have received 4 more books. Take the
number of books received by each child as x,
frame an equation in x and solve for it.​

Answer 1

Answer:

6400÷x=6400÷(x+4)+80

6400/x=6400/(x+4)+80 (LCM=x+4)

6400/x=(6400+80x+320)/x+4

6400/x=6720+80x/x+4

6720x+80x²=6400x+25600(cross multiplication)

80x²=-320x+25600

x²+320x=25600/80

x²+320x=320

x²+x=320/320

2x²=1

x²=1/2

Answer 2

Answer:

Here you go:-

Step-by-step explanation:

Let no. of books received by each child be 'x'.

No. of children = 6400/x = y ---------> (i)

y - 80 = 6400/x+4 --------------> (ii)

6400/x - 80 = 6400/x+4

6400(1/x - 1/x+4) = 80

6400(x+4-x / x(x+4)) = 80

x and -x gets cancelled out.

6400(4/ x^2+4x) = 80

6400*4 = 80(x^2+4)

25600 = 80x^2 + 320x

80x^2 + 320x - 25600 = 0

x^2 +4x - 320 = 0 (Dividing by 80)

x^2 + (20-16) x - 320 = 0

x^2 +20x - 16x - 320 = 0

x(x+20) - 16(x+20) = 0

(x-16) (x+20) = 0

Therefore, x = 16; x = -20( but it is rejected since the quantity cannot be negative)

Therefore, 16 books were received by each child.