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
[tex]P = \frac{n+2}{n+8}[/tex]
We want [tex]P = 0.60[/tex]. So
[tex]0.6 = \frac{n+2}{n+8}[/tex]
[tex]n+2 = 0.6*(n+8)[/tex]
[tex]n + 2 = 0.6n + 4.8[/tex]
[tex]n - 0.6n = 4.8 - 2[/tex]
[tex]0.4n = 2.8[/tex]
[tex]n = \frac{2.8}{0.4}[/tex]
[tex]n = 7[/tex]
He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.
