Competition participants

In the mathematical competition, its participants solved two tasks. Everyone solved at least one problem, while 80% of the participants solved the first problem, and 50% solved the second problem. Sixty participants solved both tasks. How many participants did the competition have?

Final Answer:

n =  200

Step-by-step explanation:

$$\begin{gathered} p=80+50-100=30\% \\ c=60 \\ c=p/100\cdot n \\ n=c/p\cdot 100=60/30\cdot 100=200 \\ a=80/100\cdot n=80/100\cdot 200=160 \\ b=50/100\cdot n=50/100\cdot 200=100 \\ m=a+b-c=160+100-60=200 \end{gathered}$$

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