In baseball, the batting average is determined by dividing the number of hits by the number of at-bats. We know that Harry is playing in a game in which he starts with a batting average of .262. In the current game, he goes three (3) hits out of five (5)...

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In baseball, the batting average is determined by dividing the number of hits by the number of at-bats. We know that Harry is playing in a game in which he starts with a batting average of .262. In the current game, he goes three (3) hits out of five (5) at-bats. With these metrics, he ends the game with a batting average of .278.

We are given enough information so that it is possible to find the number of hits and at-bat before and after the game. With the data we are given, we can establish an algebraic equation. We can use “X” to represent the number of hits and “Y” to represent the number of at-bats, so that the player’s batting average equals X divided by Y.

We also know that prior to the current game, X / Y equaled Harry’s batting average of .262. In the current game, Harry is at-bat five times and hits the ball three of those times, ending the game with a revised batting average of .278. Thus, substituting X for hits and Y for at-bats, we know that

*X divided by Y = .262*

And

*(X+3) divided by (Y+5) = .278.*

We can arrange the metrics to isolate either X or Y and solve the equation. For example, using Harry’s batting average prior to the latest game, we know that X divided by Y equaled .262. We can multiply both sides of this equation by Y to get X=.262 multiplied by Y, or .262Y. This enables us to eliminate X and use Y throughout our work in order to solve the equation. Specifically,

*(.262Y*) + 3 divided by (Y+5) equals .278.*

In this particular case, we need to round because solving the equation does not yield whole numbers.

*Remember, we are using this fraction to replace X, as they are equivalent.