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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 - Mathematics

Sum

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?

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Solution

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.

Concept: Applications of Determinants and Matrices
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