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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?

 Dec 26, 2021
 #1
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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

 Dec 26, 2021

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