Question

A tennis player keeps track of the number of successful first serves he makes. During the first 8 service points of a game, only 2 of his first serves are playable, so his first serve percentage is 25%. How many more consecutive successful first serves must he have to raise his first serve percentage to 60%?

Answer 1

Answer:

He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.

Step-by-step explanation:

After n consecutive serves, his total number of serves is going to be n+8, since he has already served 8 times. In the best case, his number of successful first serves is n+2.

His percentage of succesful first serves is the division of the number of succesful first serves divided by the total number of serves. So

$P = \frac{n+2}{n+8}$

We want $P = 0.60$. So

$0.6 = \frac{n+2}{n+8}$

$n+2 = 0.6*(n+8)$

$n + 2 = 0.6n + 4.8$

$n - 0.6n = 4.8 - 2$

$0.4n = 2.8$

$n = \frac{2.8}{0.4}$

$n = 7$

He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.