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 Rs.10 more, however if there were 16 children more everyone would have got Rs.10 less. Using matrix method, find the number of children and the amount distributed by Seema. What values are reflected by the Seema?

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 Rs.10 more,  however if there were 16 children more everyone would have got Rs.10 less. Using matrix method, find the number of children and the amount distributed by Seema. What values are reflected by the Seema?

Filo · Accepted Answer

according to the question,Let number of children = xAmount received by one children = ytotal amount received = xy .....(1)According to first condition :If no.of children = (x - 8)Amount received by one = (y + 10)total amount= (x- 8)(y + 10)implies xy + 10x - 8y - 80 ......(2)put (1) = (2) {both are total amount}xy = xy 10x - y + 80implies 10x - 8y=80implies 5x−4y=40....(3)Accordingtothesecondcondition:IfNo.ofchildren=(x+16)Amountreceivedbyone=(y−10)totalamount= (x+16)(y−10)implies xy−10x+16y−160.....(4)put(1)=(4)botharetotalamountimplies xy= =xy−10x+16y−160implies −10y+16y=160implies −5y+8y=80......(5)Wecanexpress(3)and(5)inMatrixasfollow:A=5−4−58,B=4080,x =xyAsweknow, AX=BimpliesX= {A^{ - 1}}BTofind {A^{ - 1}} ,WeneedcoffectorofA{A_{11}}=8A_{21}=5A_{12}=4A_{22}=5AdjointofA=8455{A^{ - 1}}=1AAdjointofA impliesA−1=1208455 impliesA−1B=120320+320200+400 implies itA−1B=3230....(7) From(6)and(7),Wegetxy = 3230So No of children = 32Amount got by one children = 30Total Amount = 960

Question Text	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 Rs. $10$ more, however if there were $16$ children more everyone would have got Rs. $10$ less. Using matrix method, find the number of children and the amount distributed by Seema. What values are reflected by the Seema?
Answer Type	Text solution:1
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