1550.23 – Batting Average no. 1

Shortstop Omar has been officially at bat 322 times this season and has a batting average of 0.289 (which is the number of hits divided by 322). He is guessing that he will have 53 times at bat before the season ends. He would love to end the season with a batting average of .300. How many hits should he get out of the remaining 53 at bats to make this happen?

Solution

.289 average for 322 at bats means he has had 93 hits. He thinks he will have a season total of 322+53=375322 + 53 = 375 at bats, and he wants a batting average of .300. This means getting .300×375.300 \times 375 hits, which is 112.5 hits. He'd better get 113. This means that he needs 113−93=20113 - 93 = 20 more hits, out of his 53 at bats. (2053=.377\dfrac{20}{53} = .377 – the batting average he'd need to have for those last 53 at bats if he's going to make .300 overall. He'll really need to fire up.)

(Since 53 is just a guess, it would be interesting to program a spreadsheet to see what Omar has to do, given a different number of remaining at bats.)