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.