rational expression question

Question

Part way through the season, a batter has recorded 56 hits in 178 at-bats. But for the rest of the season, he gets hits in all but 224 of his remaining at-bats, and his batting average increases to approximately 0.336. Determine algebraically how many hits he gets in total for the season.

 

batting average = the number of hits divided by the number of at-bats. His original batting average would be 56/178 = 0.310.

Answer 1

One way to set this up is  Let X = # of remaining AB so X-224 is # hits in those remaining AB.

 

Then overall BA is  0.336 = [56 + (X-224)] ÷ [178+X]

 

Solve this for X (and remember that total # hits will be 56 + x-224