Question

Shveta distributed y kg rice and x kg wheat to each family which comes under BPL of her society where x and y are the natural numbers which satisfy 8x + 3y = 96 and x < 5. If number of beneficiaries family is 30, then find the total quantity of rice and wheat respectively distributed by Shveta.​

Answer 1

Given :  

Shweta distributed y kg rice and x kg wheat to each family which comes under BPL of her society where x and y are the natural numbers which satisfy 8x+3y =96 and x<5 .

The number of beneficiaries family is 30

To  find   :  the value of x and y respectively distributed by Shweta​

x<5

x is natural number hence x can be 1 , 2 , 3 or 4 only

8x +3y =96

x = 1  => y  = 88/3    not a natural number

x =2  => y  = 80/3   not a natural number

x =3  =>  y = 24       not a natural number

x = 4 => y  = 64/3  not a natural number

Hence x  = 3   and y = 24  is only possible solution  

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Answer 2

Given :- x and y are the natural numbers which satisfy 8x + 3y = 96 and x < 5. If number of beneficiaries family is 30, then find the total quantity of rice and wheat respectively distributed by Shveta.

Solution :-

→ 8x + 3y = 96

since x is a natural number and x < 5 . putting value of x as 1,2,3 and 4 we get,

at x = 1,

→ 8 + 3y = 96

→ 3y = 96 - 8 = 88

→ y = 88/3 ≠ not a natural number .

at x = 2,

→ 16 + 3y = 96

→ 3y = 96 - 16 = 80

→ y = 80/3 ≠ not a natural number .

at x = 3,

→ 24 + 3y = 96

→ 3y = 96 - 24 = 72

→ y = 72/3 = 24

at x = 4,

→ 32 + 3y = 96

→ 3y = 96 - 32

→ 3y = 64

→ y = 64/3 ≠ not a natural number . .

therefore, x(wheat) = 3kg and y(Rice) = 24kg.

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