Donna had some candies. She kept half of the number of candies plus
3 candies. She gave the remaining candies to Jane. Jane ate 1/3 of
the candies plus 4 candies. Then Jane gave the remaining candies to
Kate. Kate ate 1/4 of the candies and had 42 candies left. How many
candies did Donna have at first?
+313 Let say Donna has x candies
Now, she kept half the number
of candies plus 3 candies
i.e. (x/2 + 3)
She gave remaining candies to Jane
i.e. x - (x/2 + 3) = x/2 - 3
Jane ate 1/3 of the candies
plus 4 candies
i.e. 1/3 (x/2 - 3) + 4 = x/6 + 3
Jane gave remaining candies to
Kaye
i.e. (x/2 x 3) - (x/6 + 3)
= x/3 - 6
Kate ate 1/4 of the candies
ie 1/4 (x/3 - 6) = x/12 - 3/2
remaining candies are
(x/3 - 6) - (x/12 - 3/2)
= x/4 - 9/2 = 42
=> x/4 = 42 + 9/2
=> x = 4 (42 + 9/3)
x = 186
Now Donna kept half the
number of candies plus 3 candies
=> x/2 + 3
=> 186/2 + 3
=> 96
Donna ate 96 candies
