Question

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?

Answer 1

Answer:

Total number of trials is 35.

Step-by-step explanation:

Given : 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.  

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials $=\frac{3}{7}$

and probability of my friend's winning is  $=1-\frac{3}{7}=\frac{4}{7}$  

Let there be n numbers of trials.

Therefore, my score after n trials $=\frac{3n}{7}$

and my friend's score after n trials   $=\frac{4n}{7}$

Now, the number of trials my friend won more than me is

$\frac{4n}{7}-\frac{3n}{7}=\frac{n}{7}$

We know, that my friend won 5 more trials than me so comparing the actual and given we get,

$\frac{n}{7}=5\\n=7\times5=35$

Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

After 35 trials I will win $\frac{3\times 35}{7}=15$ trials

and my friend will win $\frac{4\times 35}{7}=20$  trials.

Hence, my friend won 5 more trials than me.