NFL passer rating The National Football League ranks its passers by assigning a passer...

NFL passer rating

The National Football League ranks its passers by assigning a passer rating R based on the numbers of completions C, attempts A, yards Y, touchdowns T, and interceptions I. In a normal situation, it can be shown that the passer rating can be calculated using the formula

(a) In 2004, Peyton Manning completed 336 of 497 passes for 4557 yards and had 49 touchdown passes as well as 10 interceptions. Calculate his record-setting rating.

(b) How many more yards would he have needed to obtain a passer rating of at least 121.5?

(c) If he could make one more touchdown pass, how long would it have to be for him to obtain a passer rating of at least 122?