Question

Paul, Kate and Sarah's mother left a bowl of jellybeans on their kitchen counter. Paul took one-third of the jellybeans, but then threw back 4 because he didn't like the black ones. Sarah ate 6 jellybeans and then took one-quater of what remained. Kate took one-third of what remained, and then picked out and ate the last 4 black ones because she really liked them. If after all this there were 6 jellybeans left, how many were there to begin with?

please explain

Answer 1

number at the beginning ----- x
Paul took (1/3)x - 4
number left after Paul's turn = x - (x/3 - 4) = 2x/3 + 4
after Sarah ate 6, number left = 2x/3 + 4 - 6 = 2x/3 - 2
took 1/4 of that, so remaining = (3/4)(2x/3 - 2) = x/2 - 3/2
Kate took 1/3 of that plus 4 = (1/3)(x/2 - 3/2) + 4
= x/6 - 1/2 + 4 = x/6 + 7/2

number left = (x/2 - 3/2) - (x/6 + 7/2)
= x/3 - 5

x/3 - 5 = 6
x/3 = 11
x = 33

check:
Paul took 1/3, which is 11, then put 4 back, so he took 7 , leaving 26
Sarah ate 6, leaving 20, then took 1/4 of that leaving 15
Kate took 1/3 of that, which is 5, leaving 10
Of the remaining, Kate then ate 4, leaving a final count of 6, as given

my answer is correct