Answer:
120
Step-by-step explanation:
Let x students are taking the contest in total.
According to the given information:
[tex] \frac{1}{3} x + \frac{1}{4} x + \frac{1}{5} x + 26 = x \\ \\ (LCM \: of \: 3, \: 4, \: 5 = 60) \\ \\ \frac{20}{60} x + \frac{15}{60} x + \frac{12}{60} x + 26 = x \\ \\ \frac{(20 + 15 + 12)}{60} x + 26 = x \\ \\ \frac{47}{60} x + 26 = x \\ \\ 26 = x - \frac{47}{60} x \\ \\ 26 = \frac{60x - 47x}{60} \\ \\ 26 = \frac{13}{60} x \\ \\ \cancel{26} \times \frac{60}{ \cancel{13}} = x \\ \\ 2 \times 60 = x \\ \\ x = 120[/tex]
