What is the total number of participants if 1/4 writing, 1/6 reading, 1/8 designing, and 33 mathematics students participated?

🧠 Explanation (Math):

Given: $tfrac{1}{4}$ writing, $tfrac{1}{6}$ reading, $tfrac{1}{8}$ designing, and 33 mathematics; total participants $= T$
Step 1: Form equation of counted participants ⇒ $Tleft(tfrac{1}{4}+tfrac{1}{6}+tfrac{1}{8}right)+33=T$
Step 2: Compute fraction sum with LCM 24 ⇒ $tfrac{6+4+3}{24}=tfrac{13}{24}$
Step 3: Rearrange ⇒ $T-tfrac{13}{24}T=33 Rightarrow tfrac{11}{24}T=33$
Step 4: Solve for $T$ ⇒ $T=33times tfrac{24}{11}=72$
Final Answer: 72