Final answer:
To find the total number of game booths when students set up 5/6 of them, divide the number of booths set up by students (30) by 5/6 to get a total of 36 booths.
Step-by-step explanation:
If 5/6 of the game booths were set up by students and we know the students set up 30 booths, we can find the total number of game booths by dividing the number of booths set up by students by the fraction they represent. So, the calculation would be 30 booths ÷ (5/6), which simplifies to 30 booths ÷ 5 × 6 = 6 booths × 6 = 36 booths in total.