Answer: 36 candies were in the bowl when the day started
Step-by-step explanation:
Let x represent the number of candies in the bowl initially.
One day sean decided to grab a handful of the candies and took 1/3 of the candies. This means that Sean took x/3 candies. Number of candies left would be x - x/3 = 2x/3.
Since he decided to return 4 of them, the remaining number of candies would be
2x/3 + 4 = (2x + 12)/3
Tracy also helped herself and took 1/4 of the candies in the bowl. This means that she took
1/4(2x + 12)/3 = (2x + 12)/12
The number of candies left would be (2x + 12)/3 - (2x + 12)/12
= 4(2x + 12) - (2x + 12)/12 = (8x + 48 - 2x - 12)/12 = (10x - 36)/12
Since she put down 3, the number remaining would be
(10x - 36)/12 + 3 = (10x - 36 + 36)/12 = 10x/12
Eugene grabbed 1/2 of the candies in the bowl. This means that he took
1/2 × (10x)/12 = (10x)/24
The amount remaining is
(10x)/12 - (10x)/24 = [2(10x) - 10x)]/24
= [20x - 10x]/24 = 10x/24
He put those two back. It means that amount left would be
(10x)/24 + 2
At the end of the day, there are 17 candies left. This means that
10x/24 + 2 = 17
10x/24 = 17 - 2 = 15
10x = 24×15 = 360
x = 360/10 = 36
