72 sweets were distributed equally among x children. if there were 6 children less each would get 1 sweet more. find number of children.
Answers
Given that,
No. of Children = X
No. of Sweets = 72
Then,
Sweet/Children N₁ = 72/X ------------------------------------------------- [1]
Further given that,
No. of Children = X - 6 [∵ 6 Children less than earlier case]
No. of Sweets = 72 [Same as earlier]
Sweet/Children N₂ = 72/(X-6) -------------------------------------------- [2]
Given that,
Every child get 1 sweet more than earlier case if 6 children are less,
N₁ + 1 = N₂ ---------------------------------------------------------------------- [3]
Apply N₁ & N₂ from [1] & [2] in equation [3]
(72/X) + 1 = 72/(X-6)
Further simplifying,
(72+X)/X = 72/(X-6)
(X+72) (X-6) + X = 72X
X² + 72X - 6X - (72 x 6) = 72 X
X² + 72 X - 6X - 72X - 432 = 0
X² - 6X - 432 = 0
Using quadratic equation solver,
a = 1 ; b = -6 ; c = 432
Refer attachment for the formula (Not feasible to type here)
Applying above value we will get,
X = 24, X = -18
Since Number of Children cannot be negative
X = 24 Children.
If we distribute 72 sweets to 24 Children, then each will get,
N₁ = 72/24 = 3 Sweets
If 6 Children less then no. of Children is 24 - 6 = 18 Children
Each children will get,
N₂ = 72/18 = 4
Its proved N₁ + 1 = N₂