Before hosting their annual Chess Tournament and Spelling Bee, a school received 7 boxes of honorary medals: one medal for every participant. After Chess Tournament, two boxes were empty and the rest were still closed. After the Spelling Bee, which had twice as many participants, there were 72 medals left. How many people competed in Chess Tournament?
To solve this problem, we can set up an equation based on the information given.
Let's assume the number of participants in the Chess Tournament is x.
According to the information given, there were initially 7 boxes of medals, with one medal for each participant. So, there were initially 7x medals.
After the Chess Tournament, two boxes were empty, which means there were 5 boxes left. Since each box initially had the same number of medals, each of the 5 boxes had (7x / 5) medals.
After the Spelling Bee, which had twice as many participants, there were 72 medals left. So, the number of medals after the Chess Tournament and before the Spelling Bee would be (7x / 5) - 72.
Given that the Spelling Bee had twice as many participants as the Chess Tournament, the number of participants in the Spelling Bee would be 2x.
Now we can set up the equation:
(7x / 5) - 72 = 0
To solve this equation, we can multiply both sides by 5:
7x - 360 = 0
Add 360 to both sides:
7x = 360
Divide both sides by 7:
x = 360 / 7
Now, let's calculate x:
x ≈ 51.42857
Since the number of participants in the Chess Tournament needs to be a whole number, we need to round this answer. In this case, we can consider that approximately 51 participants competed in the Chess Tournament.