Ross has scored a total of 311 runs in the nine games of cricket he has played this season. He has been out in all of these innings.
Michael goes in after Ross is out in the last game. To that point Michael has scored 26, 43, 22, 35, 0, 29, 63, and 21, but has only been out in 7 innings so far. What are the fewest runs that Michael needs score in this innings in order to beat Ross’ average? A batting average is calculated by dividing the runs scored by the number of times the player has gone out.
Solution
Ross’ average is 311/9 = 34.56. If Michael scores x runs for the season and does not go out in his last innings, his average will be x/7. So we need to find x if x/7 ≥ 311/9. This means that x has to be at least 311 × 7/9 = 241.88. But x has to be a whole number, so x ≥ 242.
Michael has so far scored 26 + 43 + 22 + 35 + 0 + 29 + 63 + 21 = 239. Michael then has to score at least 242 – 239 = 3 runs in this innings as long as he does not go out.
Extension
How many runs does he need to score if he does go out?