# In baseball, the batting average is determined by dividing the number of hits by the number of at-bats. Harry is playing in a game in which he stats with a batting average of .262 and goes 3 hits out of 5 at-bats. He ends the game with a batting average of .278. Is it possible to find the number of hits and at-bat before and after the game?

Harry's number of hits and at-bat before the game are 26.36375 and 100.625. After the game they are 29.36375 and 105.625. In baseball, the batting average is determined by dividing the number of hits by the number of at-bats.

Harry's batting average before the game starts is 0.262. He goes 3 hits out of 5 at-bats in the game. If his number of hits before the game is H and the...

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In baseball, the batting average is determined by dividing the number of hits by the number of at-bats.

Harry's batting average before the game starts is 0.262. He goes 3 hits out of 5 at-bats in the game. If his number of hits before the game is H and the at-bats are N, we know that 0.262 = H/A or H = 0.262*A.

As Harry goes 3 hits out of 5 at-bats during the game, his batting average at the end of the game is (0.262*A+3)/(A+5). This is equal to 0.278.

Solving (0.262*A+3)/(A+5) = 0.278

=> 0.262*A+3 = 0.278*A + 5*0.278

=> A(0.278 - 0.262) = 3 - 5*0.278

=> A*0.016 = 1.61

=> A = 100.625

H = 26.36375

At the end of the game, his number of hits is 29.36375 and the at-bats are 105.625.

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