Question

On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹ 10 more. However, if there were 16 children more, everyone would have got ₹ 10 less. Using the matrix method, find the number of children and the amount distributed by Seema. What values are reflected by Seema’s decision?

Answer 1

Let the number of children be x and the amount distributed by Seema for one child be ₹y.

So, (x − 8)(y + 10) = xy
⇒  5x − 4y = 40         ...(i) 

and 
(x + 16) (y − 10) = xy

⇒ 5x − 8y = −80        ...(ii) 

To solve (i) and (ii),

let A = `((5,4),(5,-8)), "B" = ((40),(-80)), "X" = (("x"),("y"))`     

∵ `"AX" = "B" ⇒  "X" = "A"^-1 "B"`

Now `"A"^-1`

`"A^-1 = - 1/20 ((-8,4),(-5, 5))`

⇒ `(("x"),("y")) = ((32),(30))`

Clearly x = 32, y = 30.

Hence the number of children = 32 and the amount distributed by Seema = ₹30.

Value reflected: Helpfulness towards the needy people.