Question

On her birthday seema decided to donate some money to children of an orphanage home. If there ware 8 children less, every one would have got Rs.10 more However, if there were 16 children more, every one would have got Rs.10 less. Using matrix method, find the number of children and the amount distributed by seema.

Answer 1

Answer:

Step-by-step explanation:

Given On her birthday seema decided to donate some money to children of an orphanage home. If there ware 8 children less, every one would have got Rs.10 more However, if there were 16 children more, every one would have got Rs.10 less. Using matrix method, find the number of children and the amount distributed by seema

Let the amount to be donated by Seema be x and number of children be y

So amount of each child will be x / y

if 8 children are less everyone would get 10 Rs more, So

   x / y - 8 = x / y + 10  

  5 y^2 - 40 y = 4 x---------(1)

If there were 16 children more every one would get Rs 10 less, so

 x / y + 16 = x / y - 10

So we get  - 10 y^2 - 160 y = - 16 x

5 y^2 + 80 y = 8 x -------------(2)

Upon dividing (1) and (2) we get

5 y^2 - 160 y = 0

y = 32

substituting for y we get

x / 32 - 8 - x / 32

x = 960

Amount to be donated is Rs 960 and number of children is 32