Miss larner had a bowl of jolly ranchers sitting on her desk. one day sean decided to grab a handful of the candies and took 1/3 of the candies, but decided to return 4 of them because he felt guilty. during the next period, tracy also herself and took 1/4 of the candies in the bowl, but she felt too guilty and put 3 back. after lunch eugene grabbed 1/2 pf the candies in the bowl, but noticed two looked like they had been slobbered on. he put those two back (not because he felt guilty; he just didn't want candy that has been slobbered on. at the end of the day, there are 17 candies left. how many candies were in the bowl when the day started?

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

step-by-step explanation: