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.18. Write any three Euclid’s axioms
Answers
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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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
Solution :
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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