John has some marbles he gave 1\4 to sally and 1\2 of the remainder to marry. If john remained with 20 marbles. How many marbles John had at the beginning

2 answers

So we know that he lost 1/4 + 1/2 of his marbles which would be equal to 3/4 of his marbles so we would take 1 and subtract 3/4 to get 1/4 so that means that 1/4 is 20 so 20 x 4 = 80

1/4 + 1/2 = 3/4
1 - 3/4 = 1/4
1/4 = 20
1 = 80 :)
original number of marbles ---- x
he gave away:
(1/4)x to Sally , leaving him with (3/4)x

(1/2)(3/4x) to Mary, leaving him with 20

x - (x/4 + (3/8)x ) = 20
times 8 to clear those nasty fractions
8x - 2x - 3x = 160
3x = 160
x = 160/3 , not a whole number, suspect a typo or a bogus question

NB, 80 is not the correct answer since it does not check out:
e.g.
start with 80 gives 1/4 or 20 to sally , leaves 60
gives half of 60, or 30, to Mary, leaving him with 30, not 20!!

my answer: 160/3 marbles
1/4 of 160/3 is 40/3, leaving him with 120/3 marbles, or 40 marbles
gives 1/2 of 40, to Mary leaving him with 20 as required.

So even though mathematically it works out, the question is poorly
designed and not realistic