You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how many trials are in the competition?

We have been given that me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.  

Probability of my winning is and probability of my friend's winning is .    

Let there be n numbers of trials. Therefore, my score after n trials is and my friend's score after n trials is .

Therefore, trials my friend won more than be would be,

We have been given that my friend won 5 more trials than me. So upon equating these two quantities we will get,

Therefore, total number of trials is 35.

Let us verify our answer.

After 35 trials I will win trials and my friend will win trials. Hence, my friend won 5 more trials than me.