on her birthday shree decided to donate some money to the children of an orphan home if there were eight children less everyone would have got rupees 10 more however if there where 18 children more everyone would have got rupees 10 less. Using matrix method find the number of children and the amount distributed by shree.
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Answers
Answer:
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Step-by-step explanation:
according to the question,
Let number of children = x
Amount received by one children = y
total 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 + 80
implies 10x - 8$$y = 80
implies 5x - 4y = 40 ....(3)
According to the second condition:
If No. of children = (x + 16)
Amount received by one = (y - 10)
total amount = (x +16)(y- 10)
implies xy - 10x + 16y -160 .....(4)
put (1) = (4) {both are total amount}
implies xy= =xy -10x + 16y
- 160
implies -10y + 16y= 160
implies -5y + 8y = 80 ......(5)
We can express (3) and (5) in Matrix as follow :
A = 5-4-58, B = 4080, x = xy
As we know,
AX = B
implies X = A
−1
B
To find A
−1
, We need coffector of A
A
11
= 8
A
21
=5
A
12
=4
A
22
=5
Adjoint of A = 8455
A
−1
= 1 AAdjoint of A
impliesA-1 = 1208455
impliesA-1 B = 120320 + 320200 + 400
implies it A-1 B = 3230 ....(7)
From (6) and (7), We get
xy = 3230
So No of children = 32
Amount got by one children = 30
Total Amount = 960