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
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
To find the number of marbles John had at the beginning, we need to work backwards from the information given.
Let's assume that John had x marbles at the beginning.
John gave 1/4 of his marbles to Sally, which means he gave away (1/4)*x marbles.
The remaining marbles after giving some to Sally would be x - (1/4)*x = (3/4)*x.
John then gave 1/2 of this remaining amount to Marry, which means he gave away (1/2)*((3/4)*x) marbles.
The remaining marbles after giving some to Marry would be (3/4)*x - (1/2)*((3/4)*x) = (3/4)*x - (3/8)*x = (3/8)*x.
According to the given information, John remained with 20 marbles, so we can equate the remaining marbles to 20 and solve for x:
(3/8)*x = 20
Multiply both sides of the equation by 8/3:
x = (20 * 8) / 3
x = 53.33 (rounded to two decimal places)
Therefore, John had approximately 53 marbles at the beginning.